So, if you cannot play the real GMod, what can you play?
If you have a PS Vita (which can run PSP games and homebrew), you can install (PSP emulator for Vita). Then use Moonlight or a similar streaming app to stream real GMod from your PC to the Vita. The Vita's second analog stick makes it playable. gmod psp
A major source of confusion for the search is the PlayStation Vita. Many users mistakenly search "GMod PSP" when they mean "GMod on Sony handhelds." So, if you cannot play the real GMod, what can you play