Well it won't anymore now that you told her! :P
Games can definitely be scary, I think any gamer that's played a "scary" game alone, at night, with the lights off can attest to that fact. The scariness comes from getting really into the game, which involves A LOT of factors, but when the stars align, and you connect with the game, there's no other experience like it.
I think you've done a pretty good job grabbing the essence of what is scary in video games, it's the tension that you might die at any moment, and what the heck you're going to do next to survive. If you go back and play the original Resident Evil games they're probably not that scary at all, precisely because of the lame puzzles.
But is fighting for your life scary or just tension? What is scary? There's also creepiness. I think if you play any of the games outlined here and get into them you'll be really scared. Where I consider that getting your heart pounding, and your palms sweating, but not keep you up at night psychological terror.
And for the extra-bit of creepiness check out Bioshock. It's the spiritual successor to System Shock, and it looks CRAZY! I warn you though, the footage could be a little disturbing...