Um...pretty much every game that isn't VR or a quick competitive shooter/RTS?

Don't play 3D hologram games, like those show in the Star Trek TV-series. You'll LOOOOOSE.

How about adventure games? Some are 2D, some are 3D, but strong depth perception is rarely needed. "Pixel hunting" for usable objects is rarely needed in modern adventure games.

Some sort of pirate games? Just kidding. (horrible)

I would think hack and slash games would fit.

Turn-Based 4X games.

In theory you can see a whole computer screen at once with one eye, and you don't need any kind of depth perception unless playing with some VR set (which won't be the case...) so technically any game would be fit. In any case, it would be better to avoid games where your gaze can be turned too quickly from one point to another one, like a fast FPS or similar.
Any adventure, RPG or strategy game will be OK.

Point and Click games... GOG has a lot of them and something might interest you

Point and Click

Why should that be a problem? The screen is flat so the information your eyes receives isn't in 3D with depths anyway, it's only your mind that creates the illusion that it is 3D. But yes, 3D screens and VR headsets that actually uses both the eyes will naturally be a hinder to for you, at first at least.

Though, you can perfectly train yourself to handle it without depth perception. I have a friend with one glass eye and he drives normally, so it's very common to manage without it.

Really any game that doesn't require 3D-glasses or some other stereoscopic technology.

Anything but FPS really...

heh , how do you get depth perception from a 2d screen?
btw fps needs no good eyesight , it needs good cheats to aim and show enemy for u

Ummm. depth perception isn't a thing in gaming except in stereoscopic 3d (3DS, or glasses) or VR. Other than that, depth is exactly the same for both eyes in games with 3D rendering.

visual novels?
point and click games, as already mentioned?
some not fast paced RPGs?
Kynseed?

That sounds like quite the bind, hope it's nothing too serious. In any case, you can probably deal with anything that's relatively static and not fast moving - a good time to get into RTSes or TBSes. Try the Anno series, if you haven't already. Heroes of Might & Magic III is also a good option (and an all time best seller on GOG).

You are right, of course. However, it can affect your FOV depending on the size of your monitor (sometimes even the sharpness of your vision), and get old very fast if you're playing fast paced stuff. As with all things in life, we tend to take this stuff for granted until it becomes a problem.

P.S.: I can somewhat relate to this due to a case of eye infection I had in the past.