My girlfriend is from the same cloth of not understanding the joys of games. However, she's insanely competitive and hates being rubbish at something. So on the few occassions I've tried it's always ended really badly.
First there was the Blue Toad Murder Files as I got them free with Ps+. She did actually enjoy those. Mario Kart was a no go because she wouldn't accept the fact she was losing. Tried Gt5 with a wheel, told her she could pretend to drive a fast car. That turned out to be one of the more bizarre hours of my life. Me and my mates have a Top Gear style leaderboard for taking the Go-Kart around Autumn Ring Mini. We'd all just sit around doing a few laps each trying to beat the ghost. Well, she refused the ghost, wouldn't listen to anything about where to brake, or advice on lines to take. Why? Well apparently that would be cheating. So I had to sit in silence while she swore at the game for being nothing like driving, while having a go at me for encouraging her to play it because "I know how competitive she is!"
We've not tried again since.
My solution... I bought a laptop. The Tv (and with it the underused PS3) are hers now