You should look into method swizzling/hooking, to hook into a c++ method called on every frame, and add a line of code to save the frame buffer to disk. You can either do this at runtime via some kind of code injection, or at compilation time if you can manage to re-sign the game.

I don't know much about c++ reverse engineering but I've done this when reversing iOS apps (and this is what "tweaking" means in the jailbreak community). The same concepts should apply.

The first step is obtaining a class dump (what it's called with iOS) that shows you all the header files and gives you the information necessary to understand what's going on in a debugger so you can determine which method to hook.

Edit: this should point you in the right direction - https://rafalcieslak.wordpress.com/2013/04/02/dynamic-linker...