colonization, fantasy general, FTL, the last federation, original war, alpha centauri, zak mckracken...
perhaps also Deponia series and... https://www.gog.com/game/the_interactive_adventures_of_dog_mendonca_and_pizzaboy

If they like puzzles:

Sokobond - simple, minimalistic but great fun. No chemistry knowledge required.

Oh yes, Gabriel Knight, very good suggestions:)

My mom liked Pinball Gold.

Spacechem is fantastic, but it do require about 10 minutes of tutorials before you get to the actual game, and there is a point in the tuts where I always get stuck. It's the same with a lot of other games - you have to tediously learn the mechanics before the fun begins.

Flatout 2, if the computer can manage. Racing games are plenty easy to understand. and good graphic is always a plus. A wheel is hightly recommended, though.

Don't Starve is quite intuitive, you can just start playing right away.

Another idea occurred to me.

How about the D.R.O.D. series? I haven't played any of them yet, but I hear that those games are turn-based puzzle games, and are therefore not a bad choice for an intelligent grandma. (I hear those games are challenging, but not in a way that requires reflexes or similar.)

i made a BattleShip in Java, if you want just pm me.

There's a reason why elderly people enjoy playing hidden object games. I know they're considered utter trash by hardcore gamers, but they have a bit of a community of their own built around them and some are actually supposed to be quite good. Then again, you'll probably need to install Steam to run them properly.

Huniepop with uncensored patch.

DROD.

It's turn-based so you don't need good reflexes to play it and it is one of the best puzzle game series out there. Which means it will keep your mind busy. The first DROD pack (including DROD 1-3) should also keep you ocupied for about 300 hours and that's probably one of the best price: gaming time ratios you'll find on GOG.

Tripletown, card city nights.

Basically any point & click adventure really. They often have nice puzzles and a great engaging story. Also turn based strategy games. Turn based rpgs could also be a viable option. If you look into these genres, you'll find plenty of games. I could list a lot of nice games but a lot has already been suggested.

My mother like HOGs, puzzle games and platforms like Mario. She also playes the odd jRPG now and then. She is very much into Farm Ville 2....

I have a friend pushing 70 who adores Diablo 2 but she's kind of weird, and D2 isn't here anyway so it's kind of moot.

Jack Keane 2 transcends age.