"Allowed" is not really the issue. If Peerplays holders vote to fork a new game into the native code, then it will be forked in. (Of course we are talking about on-chain games here. Remember the other half of Peerplays is the server-side model which will let users play pretty much any game in the world, as long as there is a host.)

So for on-chain games, the community needs to determine if there will actually be a market for that particular game. Take chess for example; How much money is wagered every year on online chess games? I imagine chess is not a "low hanging fruit" as far as profit potential. Adding to this, the fact that bots will surely come to dominate in such a game is a recipe for failure in terms of the primary objective of the network (making a profit). Especially if you compare chess to so many other games out there that people are regularly playing for money, and which bots do not give much of an edge.

Perhaps such games will eventually be included anyways, down the line. Besides the random player matching algorithms, Peerplays also lets players pre-select their opponents, which means as long as you trust your opponent (ie. your friend) isn't running a bot and scamming you, then you could play this way. But again, is there a huge market for this?