For other people wondering what's _actually_ inside this thing, here's the "Service Source" documentation:
http://tim.id.au/laptops/apple/legacy/performa_500_series.pdfI don't know much about CRTs (except that they'll more or less kill you if you don't know what you're doing), but I do know that you're going to need to use that analog-board..
To figure out _how_ to use the analog-board, you're going to need an oscilloscope (unless you can find the schematics) to probe the signals between the main-board and the analog-board, and figure out which signals are where, and at what timings and levels.
Once you know that, you'll need to get whatever game-console you wanted to put in there, and see if you can extract those exact signals from it somehow.
Unfortunately, most likely, you won't be able to, as pretty much all game-consoles are meant to drive a TV, whilst what's in the Performa is a monitor. The monitor in this case has a resolution of 640x480, meaning, it's not one of the standard TV signals (PAL/NTSC), nor is it a multiple thereof.
As the trinitrons have an aperture grille (does all CRTs have them?), even if you somehow manage to drive it with different timing (NTSC for example), the picture would be "blurry", as the pixels won't line up with the grille.