Games and Languages
Evidently, play evolved among animals, including humans: there is a “ludic instinct”. The most likely explanation for this fact is that play provides the opportunity to practice skills that will be useful in the animal’s life—hence its appearance during childhood. But games in the formal cultural sense are not among the instincts of animals; nor are games conspicuous in the animal kingdom. There is no instinct for chess, say, and chess does not exist in animal societies. Games are structured activities governed by rules and these rules have a specific character, namely that they involve the overcoming of unnecessary obstacles toward achieving a goal.  For instance, the game of golf is constituted by rules that forbid the direct placing of balls in holes—the balls must get into the holes by means of clubs wielded from a distance, not merely by dropping them in by hand. A game is not just any old kind of playful activity. I wish to say two things about games so understood: animals don’t play games in the sense defined, and no game is innate in humans. Animals don’t distinguish between activities designed to achieve a certain goal as efficiently as possible (“technical activities”) and activities in which an artificial obstacle is created in order to serve the purposes of a game (such as the net in tennis or the handball rule in football). Animal play, which is real enough, is not governed by rules that proscribe the use of maximally efficient means to achieve a goal; presumably this idea is beyond animals. But even if something like games in this sense did exist in animal societies, they would not be instinctive; games are something additional to instinctive play. Thus in humans no games are innate, though evidently play is. No one is born knowing the rules of chess or baseball or tennis. The origin of games is not natural selection.
How then do games originate? The obvious answer is invention: people invent games. Two caveats: first, people don’t reinvent a game that has already been invented—they learn a game invented by someone else; second, the invention is not generally a one-off solitary act of creation but consists in a drawn-out sequence of actions gradually honed into the kinds of games we observe. But still, the origin is human inventiveness not genetic endowment: game competence is passed on culturally not by biological inheritance. And it is not that humans originally learned games by observing their natural environment—say, by watching some other species playing games and learning from them. No, humans create games from their own cognitive resources, as they create different kinds of technology (the wheel, the computer)—games are human inventions, neither learned nor innate. We can only invent games because we have a creative capacity—the capacity to bring new and interesting things into the world. This kind of creativity seems generally absent from the animal world, though animals can obviously learn. Animals will never invent snakes and ladders.
Thus humans have two sorts of capacity in relation to play and games: (a) an innate evolved capacity to engage in play, and (b) a creative capacity with which to invent games (this capacity is presumably itself innate, though its products are not). The innate intersects with the invented: we (instinctively) play (invented) games. Not surprisingly, then, we find a universal tendency among humans to play combined with much variation in what is played. Many different games have been invented in which to express the single universal desire to play. The innate capacity to play might itself involve certain kinds of cognitive and motor competence, and this competence could be quite complex; it is not some kind of lumpish disposition to engage in “frolicking behavior”. It might be structured and rule-governed, generative and unlimited; it might be an intricately organized computational mental module (“the play module”). The play programs might even be digital, recursive, and combinatorial. It is just that they are innate while the actual games played are invented (no innate program for billiards or backgammon). There is interplay between the two levels of psychological reality but the levels should not be conflated, and we must characterize them appropriately (innate versus invented).
The reason I am making these (I hope) pedestrian remarks is that I want to make an analogy to a far more contested area—language. I want to say that the general human capacity for language is innate but that individual languages are invented—as play is innate but games are invented. The first claim is familiar and I won’t defend it: I shall simply assume that humans are equipped with an innate cognitive structure with the formal characteristics of natural languages (notably recursive syntactic rules and a finite lexicon that combine to produce infinitely many potential sentences).  You can think of this structure as a language of thought: call it LANGUAGE. It is not identical to any human natural language, being more abstract than such a language; it is best understood as a formal computational system instantiated in the brain and deriving from the genes. It is not spoken: whatever its lexicon is the elements of it are not parts of ordinary speech. For concreteness, you might think of it as like a logical language along the lines of quantified modal logic (or whatever your favorite logic is) couched in inscrutable symbols. It is the secret code in which thought expresses itself—the universal medium of mentation. It is not an external spoken language, not even being hooked up to the vocal articulation system. Indeed, it is not inherently communicative but rather a device for expediting reasoning—a tool of thought. Thus LANGUAGE has nothing essentially to do with languages, i.e. spoken systems of human communication. LANGUAGE might have existed without languages ever coming to exist: an internal cognitive structure serving thought but accompanied by no outer system of audible signs. Similarly, play (even complex play) could have existed without the existence of games in the sense defined above; they are something superadded, by no means presupposed. Games incorporate play, but they are not entailed by play. No doubt languages likewise incorporate LANGUAGE, but they are not entailed by LANGUAGE.
Now I can state my main thesis: languages are invented while LANGUAGE is innate.  Humans found themselves genetically endowed with an internal language of thought and on that basis they erected spoken communicative languages—the former was folded into the latter. Particular languages are thus neither innate nor learned (for who could have instructed the original speakers?); they exist by virtue of human inventiveness. Note as before that this inventiveness is not to be conceived as a singular all-at-once feat of mental construction; it is rather the kind of long drawn-out haphazard process that other cultural inventions are (art, law, politics). But it is still invention, still the exercise of human creativity (not innate endowment or observational learning). Languages are indeed still being invented, reconfigured, changing and growing by human will. They are not like LANGUAGE, the fixed innate system inherited from our ancestors after some freakish genetic mutation and subsequent natural selection. The two sorts of symbolic system have quite different kinds of origin—just like play and games.  That both deserve to be called “language” is neither here nor there: that is a structural description neutral on the question of origin. When languages were invented humans exploited a pre-existing fact about themselves—an internal cognitive structure they did not invent. They linked this structure to the organs of articulation to produce a sound system (possibly a sign system) capable of expressing syntactic combinations—a highly nontrivial task. There was no guarantee that the resources of the vocal system could match the internal structure of LANGUAGE, and indeed some modifications and upgrades were called for. The reason humans invented languages, using LANGUAGE as template, was presumably for purposes of interpersonal communication (though possibly external language further helped as a tool of thought): people had to speak to be heard, i.e. to convey messages–there being no such thing as telepathy. People invented languages as a tool of communication by tapping into a LANGUAGE they did not invent. Hence there are many languages and only one LANGUAGE—as there are many games but only one play instinct (per species). Games and languages are thus part of culture, while play and LANGUAGE are part of biology. Games and languages are products of our inventive faculty, while play and LANGUAGE have their roots in biological evolution (mutation and natural selection). 
To the old question of how “language” evolved we must split the answer into two parts: (a) how the internal language of thought evolved; (b) how spoken languages evolved (came to exist). These are quite different questions, one question belonging to the science of biology, the other to the study of culture broadly construed. This division corresponds to traditional expectations, if not to many theories popular in the twentieth century; in particular, the concepts of innateness and invention replace the concept of learning.  If LANGUAGE is a tribute to the power of biological evolution, then languages are a tribute to the power of human invention. Clearly our distant ancestors must have been a clever and resourceful lot: they in effect created the language of Shakespeare from a cognitive system not originally designed for external use. This is as impressive in its way as the invention of the cell phone or the atomic bomb.
 Chomsky’s oeuvre is the obvious reference: see in particular Why Only Us: Language and Evolution (MIT Press, 2016; written with Robert C. Berwick) on how language evolved and the relationship between internal and external language.
 This is consistent with allowing that some aspects of our utterances are instinctual: not everything vocal is invented, e.g. groans, cries, shrieks, laughs, etc. We did not invent these noises; we inherited them. But such vocalizations are not part of language properly so-called: they are not part of the system of spoken words that combine syntactically. We invented this system—the mapping of meanings onto segmented sounds. We invented the sound-meaning pairings of English, German, Japanese, etc—though not the species-wide expressive sounds speakers of these languages also make.
 This is not to deny that LANGUAGE is embedded in languages as their scaffolding and soul; it obviously is so embedded. It is just to say that language differences originate from invention not inheritance.
 Of course children learn their native language, but languages don’t come to exist in virtue of learning as opposed to invention (unlike, say, geographical knowledge). The concept of learning was connected to empiricism, but the concepts of innateness and invention invoke quite different modes of intellectual acquisition.