My girlfriend only really plays some free to play puzzle games (Candy Crush) but has no problem with me gaming.

She did get quite interested on the original Xenoblade when I played that but the sequel hasn't caught her interest (not surprising as the story is no where near as good)

You can play games without your right hand?

Haha, was about to post that myself.

My wife is a gamer, but primarily on the console (PS1 and PS2 back in the day, PS4 now), and also on an android tablet these days.

She doesn't play many games, but when she finds a game she likes she plays it a lot. She has played a variety of games over the years from different genres, including: Theme Park World (PS1), Populous: The Beginning (PS1), Sheep (PS1), The Sims (PS2), and Red Faction (PS2). Her current favourites are: the tower defense/strategy game Plants vs Zombies 2 (Android), and the shooter Plants vs Zombies: Garden Warfare (PS4). She's already pre-ordered Plants vs Zombies: Garden Warfare 2 (PS4).

We don't play together because our gaming interests do not often converge, and I prefer to play single-player instead of co-op anyway (I would make an exception if she ever asked, but she never has).

My wife likes The Sims but since she rarely uses her desktop computer anymore, she mostly sticks to mobile games like Diamond Digger Saga. She also used to play Guitar Hero with me a lot.

I think she likes to watch or listen to me play because she just finds the games entertaining to look at and hear, along with my occasional exclamations of frustration. She's also said that if I have to have a vice, better for it to be video games than, say, going out and getting hammered at bars.

Ok, right hand joke is already taken so I will instead post seriously.

My partner likes to play wuite a lot but certainly not as much as I.
She likes PnC adventures, Telltale style of games, puzzle games, sometimes (but scarcely) building sims like Caesar or Pharaoh and we also play co-op games like Trine, LEGO games etc.
She also tried Amnesia recently but it seems it is too scary for her and doesn't seem eager to get back to it.
So I am happy with her gaming habits.
She also doesn't mind that I game, so no complaints here. :-)

My husband and I both enjoy gaming, though there are crossovers and diversions in our interest. Playing Hyrule Warriors co-op together is pretty fun, and we do try to use some strategy. I got him into Pokémon recently and I feel a little bad for introducing him to that kind of "drug".

Curious whether homosexual male couples have a generally better chance of having both partners enjoy gaming.

Earlier she was even interested to see what I am playing, but nowadays it is more like she tolerates my gaming habit, as long as I don't neglect my duties at home and restrict it mostly to after 10pm or so. It also seems to help her tolerate it if I play in the living room (using headphones), and don't retire to a separate room. Then she can still talk to me occasionally, ask me to do something and generally feels I am present.

She sometimes "jokingly" complains that I play too much, but then she seems to still play Candy Crush quite a lot herself on her phone... Also she seems to count all the time I am with a laptop as "gaming", e.g. right now when I'm writing this. So what, she is constantly using Facebook on her phone.

Easy, don't have one.

Genetics is constantly nagging me to get a girlfriend, I ignore it and spend a week in a Arma 2 simulation with zero nagging to do things or buying a new kitchens.

Lone wolf here.

My wife doesn't like to play games, she mostly has to listen about them from me. I bore her to shiet telling her about every damn game I play. I manage to get her playing "easy" 2d games like Shovel Knight, They Bleed Pixels or Super Meat Boy from time to time, but every time I got her to play, she nearly broke my gamepad in frustration :D

Haha, I really enjoy the diversity among people's responses!

For the most part, my own partner seems rather ambivalent towards video games. However, she doesn't seem to like when I play online with a headset...

I used to play Mario Kart Wii with my wife quite a bit before we had kids, but in general gaming is nowhere near the top of her list of interests. I get more traction with the kids.