If she games or liked games, it shouldn't be too hard to find something she might be interested in.
If she doesn't game, but is interested in it, start her off with shyt where the mechanics ain't too taxing.
I've gotten girls 'hooked' on the following.
Dredge.
Papers Please.
Buckshot Roulette and this gem.
It's more the experience and making choices that had them mad interesting and we talked/they screamed and had a blast.
If they can operate a shooter, go the looter shooter route.
Destiny
Borderlands
The Division and my personal fave.
Dying Light 1.
Nearly had one chick evicted from her apartment, how much she screamed the first night out playing Dying Light 1.

She used to come over with an overnight kit 'cause she wanted to get down on it but would be too spooked to drive back home, up and around hills just shook.
Also, you can't go wrong with Overcook 1/2 Moving out 1/2 and the other similar game called Shipping Co or some shyt like that.
Forming strategies to get the shyt done can be awesome.
One person preps the dishes, the others get the ingredients and avoid the hazards.
Good shyt.