Depending upon the game, basically none. You could make something like Farmville with an 8th grade education (excluding the computer programming skills, of course). If you want to program graphics explicitly, then you need basic trig and geometry, which I guess are also 8th or maybe 9th grade.
>>7647191 For a proper game, you need linear algebra for the graphics. Also you should probably have some advanced knowledge of solid state theory to model basically every object in the game correctly. I recommend DFTB since it is more efficient than basic density functional theory, but for charge transfer excitations in some organic molecules (like in plants) you should use TDDFT with long-range corrected functionals. I think for the nuclei classical mechanics is okay and everything fluid could be done with Navier-Stokes. For PDEs I'd prefer pseudo-spectral methods, for newtonian physics there's velocity verlet.
>>7647191 Depends on the type of game, depends on the engine, and depends on what you want to do.
For example, if you want to implement semi realistic fluid dynamics for some sort of water area, you'll need some understanding of physics and mathematics. It's the same to an extent with custom lighting, or altering models in realtime. If you're just going to be using whatever capabilities the stock physics engine has, and just working within what the engine already affords, you'll probably be fine without it.
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