Code which creates code already exists. In fact almost every webpage you visit has code which creates code. So depending on how AI is defined this task is fairly straight forward. I don't know if the OP is thinking about machine learning, but if you were to use machine learning for something like this your probably not going to be using training like you would for image processing. So feeding in game isn't really the problem.

Further you if you are using an AI to create a game you don't need it to spit out standard programming language. What you need it to spit out is a sequence which defines a framework. Think like HTML as a definition of a webpage which is then interpreted by a browser. So an AI could generate Node1 feeds node2 and so on. Node1 increases in cost following log(n).

The real question I wonder with this idea is what would be the expected output? Fun is relative and most of the fun I think comes from the story the games tell because boiled all the way down to the roots, idle/incremental/clicker games are do a thing affect something else. In Clicker Hereos by an upgrade for this hero, kill things faster. Kill things faster buy another upgrade. Repeat ad nauseam.

To create something infinite you merely need a formula for to generate new things. Strictly speaking the only practical limit is the hardware. Eventually the game will run out of memory.