In The Self as a Responding—and Responsible Artifact. Ann. N.Y. Acad. Sci. 1001: 39-50. doi: 10.1196/annals.1279.003 Dennett writes as follows.
Non-human animals can engage in voluntary actions of sorts. The bird that flies wherever it wants is voluntarily wheeling this way and that, voluntarily moving its wings.
But Dennett doesn't consider this Free Will.
Humans differ from every other species in that we represent our reasons to ourselves and others. This is what gives us the power, and the obligation, to think ahead, to anticipate, to see the consequences of our actions, to be able to evaluate those actions in the light of what other people tell us, and to share our wisdom with each other. That’s what makes us free in a way that no bird is free.
[Evolution produced] creatures capable of considering different courses of action in advance of committing to any one of them, and weighting them on the basis of some projection of the probable outcome of each. In the quest by brains to produce a useful future, this is a major improvement over the risky business of blind trial and error, since, as Karl Popper  once put it, it permits some of your hypotheses to die in your stead.
Dennett calls this the only kind of free will worth having.
Computer programs that play games have this sort of capability. Does that mean that Dennett would attribute Free Will to game-playing computer programs?
I see this question as very similar to but not quite the same as the one about compatibilism. As I understand it compatibilism is the position that an agent has free will if its actions are determined (to the extent possible) by its internal state. ("To the extent possible" intends to rule out the argument that one does not have free will if one wishes to fly but cannot for physical reasons.)
I would guess that compatibilists would claim that the birds in Dennett's example have free will: their actions are determined (to the extent possible) by their internal states. But Dennett does not attribute free will to those birds. So Dennett's position and generic compatibilism (as I understand it) a somewhat different.
The underlying issue, though, seems to be essentially the same: if an agent's actions are determined (to the extent possible) by its internal state does it have free will? The only thing Dennett adds to that is that the agent's internal processing capability must include the ability to "think ahead."
So it would seem that both Dennett in particular and compatibilists in general would attribute free will to a chess playing program.
The compatibilist question also raised the issue of learning from experience. I think that's somewhat different. But we know that some game-playing programs, for example AlphaGo, are capable of learning from experience. So adding that requirement doesn't seem to change the underlying question very much: Do game playing programs that are capable of learning from experience have free will?