My SO is not a "gamer", certainly not in the same sense that I am. She played some games incidentally as a kid (she recognised Streets of Rage and joined in for a short session when I put it on), and played Tetris Effect for a session or two and enjoyed it, I think, even somewhat miffed that I didn't tell her when I had a PSVR kit for a short time so that she could have tried it with that. However, if she could never game again, I don't think she would be particularly bothered.

But I want to share with her a bit more in my hobbies, and since getting her out for a run or a hike is a lot harder, this seemd a good avenue to go down. Obviously, the simplest solution is to ask what she wants to play, and play that together, but as I said, she's not really a gamer, so she wouldn't know about the current state of games. I could do a bit of experimentation and try different games, but I figured I'd ask you fine people here for advice.

Now, in my mind (and I could be wrong, so feel free to colour outside the lines if you think it is worth it), it would be something that can be played by connecting my laptop or PS4 to the TV would be most appropriate. Something using the controller would probably be simpler. Something without too much text on screen (she has to either suffer headaches after prolonged play, or get her glasses for that). It doesn't necessarily have to be 2 player, but it could be something we could still play "together".

Am I wrong in my criteria? Could I do something different better?

I had initially thought of Dream Daddy Simulator as a goofy non-obvious possibility, but trying it out myself initially, I realised it has a lot of text (which might still be ok if it is worth it), and while the non-realtime nature of it might make for a more casual introduction to gaming, it might also be a bit boring. I could continue with Tetris Effect, but having played through it myself earlier, even on easy it is quite challenging and could be frustrating (and doesn't have that many opportunities for "playing together").

Any game suggestions I could try? Any of you play with a (mostly non-gaming) significant other? What are your experiences?

Bad idea, if she sees what childish pursuits you're spending time on, she's probably going to leave you for someone else. Don't do it!

You could always try playing point 'n click adventure games with your significant other. The process of trying together to find solutions to puzzles allows for collective thinking and comparing points of view with each other ;)

I know adventure games are generally text-heavy, but you could try some of the text-light (or even text-free) ones, such as the Amanita design games (Machinarium, Botanicula).

edit: typo

Why can't you play and she watch? Or even watch gameplay by others together (f.ex. Gopher)? In our house we do that all the time to "share the experience".

Since we use our TV (and we have no TV channels other that the pc itself) we don't play games that have too much text (especially isometric RPG's). We actually have much fun playing FPS, horror, adventure, and point'n click games.

Worms.

If your relationship survives that, you're set for life :P.

World Of Warcraft - especially Classic - https://worldofwarcraft.com/en-us/wowclassic

It is an MMO, and it work extremely well when playing with a partner. There are some classes which has great synergy, and playing together like this, completing quests and exploring a very rich and detailed work with your SO it highly recommended.

If you are beginners, I would not instantly recommend the classical warrior/priest combo (though it works very well) as both classes in Classic are a little troublesome to start out, but rather something like Paladin/Mage, Warlock/Mage, Mage/Priest (yes.... mage is OP...), Hunter/Hunter (Beast Master / Marksman combo is under-rated, this is WoW's easy mode) or Druid / Druid (with different specs).

another way of gaming together (i've done this with an ex, and a friend of mine and his wife often play this way):
you play the game, usually something adventurey.. perhaps the witcher?
and your SO takes a more passive role, watching, but partaking in the story and telling you where to go and what to do. you do all the fiddly gaming bits and they get to experience the story and game with you without having to get frustrated with controllers et al.

usually works best on tv / couches.

This isn't exactly what you're looking for, but what about board games?

My wife isn't a gamer either but I've been able to get her involved in playing board games, which both of us enjoy equally. She would never play an RPG but she's perfectly happy playing something like Castle Ravenloft board game or Munchkins.

The one potential downside is that you need a larger crowd for most board games to be fun, but there are quite a few good board games for two players

hey, good old fighting games are really made for this. if your SO doesn't end up throwing their pad at you after a match or two, then way to go!
or, as others already suggested, adventure games are great even as "you play, SO watches". they might become intetested, wich would be good.

Maybe hidden object games, though I don't know if your significant other will need her glasses for that. You can search objects together and these games are often designed with female players as their main target.

Point and click adventure games, as pointed by previous comments, are a nice suggestion too. Perhaps something that is fully voiced, so there's not much reading involved. The Amanita Design games are a great choice, as Panaias said, they don't involve much reading.

I hope you find something you and your significant other can enjoy together, have fun! :)

I would look for some topic she's interested in and go from there.

For instance my wife is interested in history, and she enjoyed Broken Sword a lot which nicely mixed history with fiction.
She became part of our pen and paper RPG group (I'm so glad she likes it!) and then she became interested in CRPG. So she played through BG 1+2+ToB... on "Hardcore DnD Rules" no less.
Nowadays she is too tired after work for gaming, and she's also a huge TV serials junkie, so sadly gaming is very low priority for her.

Rez? :P
(someone had to say it... :P)

+1
Yes, my spouse (who used to be a good gamer) can no longer use a controller (vision and peripheral nerves are failing) and is bedridden, so this is what we do. Games that are fun to watch include Shadowrun, X-COM, and The Witcher.