A computer can emulate another computer (check this out!). A computer can, in fact, emulate a simplified version of itself. The only problem is, as the usage of the emulated computer (or CPU) approaches the maximum speed/usage of the *real* computer, the number of states that can be simulated approaches one.

Eventually, with the emulated computer under 100% load, the emulation will halt - unable to continue because it will require more memory and power than the *real* computer is able to provide it. /u/Begging4Bacon explained it very well:

The computer would have to be able to simulate itself in a random state. The random state would take up all the memory, leaving none for the hardware itself.

A cellular automaton can simulate the rules of its own world with some slowdown. Here's an example with Conway's Game of Life. (If you aren't familiar with Conway's Game of Life, you can read this for an intro.)

A program written in a Turing-complete programming language like C is capable of interpreting itself. If you wrote a C program that implemented a C interpreter that interpreted its own source code, it would run forever with an ever-growing number of recursive levels.

If we assume that the "outer world" has infinite resources, or at least apparently infinite compared to the size of the "inner world", then overall I would say the answer to your question would be yes for any game with Turing-complete logic. (There are non-Turing-complete automata that can simulate themselves as well, but that's a separate issue.) As a concrete example, Minecraft's redstone logic is Turing complete. A player in this world that acts completely randomly would be capable of potentially constructing a redstone circuit which implements a CPU and associated data capable of running Minecraft (or any other game). If the inner game was Turing complete this could be repeatedly indefinitely until one of the systems runs out of space/memory. In practice it would take longer than the age of the universe for a randomly-acting Minecraft player to construct a working Minecraft simulator. While that's obviously a very long time, the age of the universe is also just about the amount of time it took for random interactions between molecules to eventually yield humans, so it's not completely preposterous.