It's possible, but not in a PDF. PDFs support only a turing incomplete subset of PostScript, because PDF's designers thought that having a turing complete language in your document format would have performance implications. (Later, they changed their mind and added JavaScript support.)

From the computation point of view, it's possible. PostScript has integer arithmetic operations needed for x86 CPU emulation. It also has mutable byte strings, which are useful as emulated memory.

With PostScript you have zmachine.ps which is a ZMachine (zork and friends) interpreter to play text adventure games.

And OFC there's a chess engine in PS, a tic tac toe, and with patience you could even play NES games, but you might need to play with the stack a lot.