Well, first of all, I'd say which hemisphere you'd like him to focus, maybe both, but for example you could look for artistic/visual games, like those find lost objects, graphic adventures without text/conversations. Would avoid those math/calcule for now.
Games that come to mind like gawhh can't remember the name! it was one with symbols hidden on objects (reckon could be a bit demanding now), cards game like find the match/pair?
Another thing you could try is the steam filter games search, adventure/logic. Heck, even flash games could help, or some GBA (gamevoy advance) ones that be about puzzle. SNES ones too (using emulators you play them on a big screen and all)

Hmm, right hand games, little to no text, what about some of mario on wii? like paper mario, simple and fun games. What else, I'm thinking...
There also sites that allow you create figures/drawings with different colors, could look it up on my FB track (posted it quite a while ago) it could help distract him from stress and also help him overcome the difficulties. Drawing/recognizing and remembering stuff.

Maybe also there's puzzle bubble/arkanoid (could be too fast on reflexes for him now) or better yet Tetris clones, strike blocks by color and shape, could do with 1 hand. Ohh I know! check World of Goo!! it's pretty good and think it may just do!
In case you don't know it, it uses physics, colors, shapes and it's about construction; getting the goo's from point A to B. Kinda like lemmings with way better!

If I think of anything else I'll comeback and edit it!
Best of luck buddy, it sucks what happened to your uncle. Wish him a fast and complete recovery!

Maybe something from telltale games? Point and click :3

I'm sorry I can't give any suggestions at the moment that haven't already been given.

I hope he gets better soon, and it does sound like he is on the road to recovery, all the best over the next few months and take care of him ;)

maybe I am totally wrong but... I whould go for a Wii (no I have no Wii but thinking about the Situation...) so he could combine games to train Body AND mind by playing...

maybe try a mobile game or app? if you want to use a pc game, try one of those simpler games like super hexagon or VVVVVV.

Jack Lumber, can be played on phone/tablet with one finger.

But if his movements are still slow, better stick to point and click adventure games or something else that does not require speed.

The only one I can recall now is Little Inferno. I loved that game and it's really simple. It is also available on Android and I bet it is also available for Apple products.

So he needs some casual games that can be played with 1 hand and don't require fast pacing/timing. That would be something like:

Toki Tori is numbah 1 http://store.steampowered.com/app/38700/
Poker Night? http://store.steampowered.com/app/31280/?snr=1_7_15__13
Tidalis / bejeweled-like games Tidalis
Puzzle Quest 1? (a favorite of mine) http://store.steampowered.com/app/12500/?snr=1_7_15__13
Faerie Solitaire Not Girly
There are a couple of MMO card games like Solforge and Might and Magic Online
And there's some turn based strategy shooters Frontline Tactics if you'd like some guns.

Hopefully any of these help. Good luck!

Proteus springs to mind. The default control are standard first person wasd, but it should be easy enough to rebind for one hand. It's a lovely experience (the kind that some people don't even like to call a 'game') about exploration, discovery, and change. Abstract and simple enough that it should be accessible to nearly everyone .

PixelJunk Eden http://store.steampowered.com/app/105800/ I think the game is slow pace and relaxing. I hope he keeps gettin better.

I doubt he wants to play games. Buy the guy some tug-mags, he only needs one hand for those.

The Cat Lady.

I'm sorry for your uncle, we all should pray. I think FEZ is a great game for that, it's simple and fun. Limbo could also be the way to go.

Bejeweled 3 and other match 3 games.
Puzzler World 1 & 2
Eufloria is a pretty simple strategy game. It even has a slower game mode.

I would say Puzzle Quest 1 and 2. Two is a little easier.

Peggle, Bejeweled, etc for something simple. Point and click adventure games, or Diablo clones if his left hand ever gains some movement and can press 1-4 for abilities. Walking Dead if you're sure he's understanding what he is seeing (anything with monsters probably should be used with caution).

I could be way off. Good luck!

I'd also suggest Chess or Checkers. They are games that stimulate brains and are generally considered to enhance memory and logical thinking. So they would be both for fun and support the recovery. All the best and prayers for your uncle.

I recommend faster than light. You can pause the game and issue commands at any time. Although it is a bit hard.

I would say puzzle/tactics games, easy ones preferabily but a bit challenging, it would be a good feeling for him to solve a puzzle even with his current limitations.

I also wouldn't discard generes just because they usually are played in a different way. When I was a kid my mother used to take away the keyboard and mouse of my computer to ground me without playing, in a short time I was playing half-life with a sidewinter joystick(joystick to aim, round button with 8 directions on top for movement, ...).

Having said that:

Audiosurf: slow songs and easy/normal dificulties. My mother and my grandmother both played it for a while, and my grandmother isn't specially agile.

Portal: give him a mouse similar to a razer naga or something like that and he should be able to play some easy maps.

Scriblenauts: if he's capable of writing.

XCOM EU: The game requires little to no reflexes, has a simple interface and in easy modes should be challenging enough to be entertaining without being frustrating.

World of Goo: the final levels might be confusing for him, but the first half of the game could be fun.

I don't know, there are lots of options that only change depending on to what degree he's physically or mentally impeded, but given the opportunity I would try to make him play something that challenged him a little rather than an easy game just to pass time.

Get him to stop taking statins (Zocor, Lipitor etc). They cause nerve damage so he might not be able to play any games if he keeps taking them.

monkey island games were always good(point/click)

I found Droplitz to be a soothing game to play, though he would be limited to the slower difficulties and smaller boards. The difficulty gradually ramps up over time, so the conclusion is always failure, but it might serve as a small gauge of his dexterity/focus recovery over time.

It all depends on his personal gaming interests. Finding an adventure game that moves at a slow enough pace to ensure he has time to process and interpret what is going on? That'll be pretty difficult. Visual Novels are an option, but rarely have much gameplay beyond a book with branching paths, and if you don't do your research before getting into one, it might have a randomly stapled on erotic element. I wonder if there is any good isometic "tactics" style game knocking around for the PC? Turn-based stuff might be better.

Audiosurf 1 and 2 might be a possibility too. Controls can be mouse only.

Throw in some songs he likes, or maybe even some OST's from games he used to play like MassEffect and Dragon Age. He might remember some music from those games and enjoy surfing along those tracks.

If he has trouble recognizing colors, playing Audiosurf on easiest with only one color is probably suitable for someone with his condition.

Maybe Wake or Lunnye Devitsy. There isn't much you have to do other than walk around and jump.