Tell her to suck it up and just enjoy your sophisticated, ecclectic, and impeccable taste in games/music.
Jokes aside, I see very few semi-open headdphones nowadays. Not to discourage you or anything; just be open-minded in the sense that you may get what you're looking for in a closed-back.
What people suggested here before me are good headphones, but keep in mind their sound signatures are quite different than the HD 6XX and you might find that to be detrimental to your enjoyment.
If you want to retain the sound I recommend the Sennheiser HD 599. It's marketed as open but really it's more semi-open than anything, and it'll be similar to the HD 6XX.
Otherwise, other than the ones already recommended, you can try Shure, Audio Technica, and the Meze Audio 99.
Best of luck to your search, and see if you can audition before buying.