Just to be clear, by that, do you mean scary to players? Cause, there are people who want to play or run horror game where characters are scared, panicked or in distress, but players are chill, relaxed and have fun.
Bingo. I hate watching 90%+ of horror movies specifically for this reason--I want to
see others face horror (and, preferably, grow into the kind of person who can overcome that horror) not
feel horrified. Feeling horrified, myself, would completely spoil my experience of the game and make me want to huddle up in my room under a blanket for an hour to get my emotions back to normal.
Great example: I played in a one-shot
Alien tabletop game. It's a little weird because everyone gets a pregen character to work with (sort of like
Betrayal at the House on the Hill), which has specific defined goals and such. Mine was actually a corporate infiltrator pretending to be just an ordinary worker--she was driven, focused, and ruthless, but an excellent deep-cover agent. Very different from me. But it was very interesting
playing that character. Nobody guessed what my character's real motives were--getting out with genetic/tissue samples of the xenomorph--and I tried to balance that ruthlessness and intelligence against the expected appearance of someone who was "just" a mining-ship crewman. When I finally revealed my true motives after the one-shot was over, everyone was shocked, though some of that is simply that I don't.
Actually watching a movie like the original
Alien? Yeah, not my speed.
Portraying a character trying to simultaneously show incredible steel, while also pretending to be someone else, while escaping from a xenomorph? Actually pretty awesome.
The fact that I, personally,
wasn't feeling what my character was, but could still feel
connected to a person having those feelings, was precisely what made it worth doing in the first place. I don't want to feel horrified. But it's fascinating to peer through the persona--the
mask--of someone horrified.