This. This is (almost) exactly what I was looking for! A simple, flexible horror game, easily adaptable horror system for my games. Easy to teach, easy to run.
I do have few things to point out, though:
I really don't get the logic of weapons. Why does a sword makes you more menacing (and durable in combat) and helps you in Fight Rolls, but a bow doesn't? Also, there are no rules explaining what should be done if the contestants have the same value of Menace/Escape (which might be common, supposing that these Stats usually have pretty close numbers).
Also, since you can get straight up killed in a fight, and not fall dying on the floor, I don't see much reason for getting First Aid..
About Stress and Panicking: I like the idea of you getting better at something because you are panicking (adrenaline can make miracles), but if characters spend stress to do so, they might never gain a scar at all, unless they witness some real lovecarftian horror to immediately get a scar. MAYBE another interesting approach would be if they could GAIN stress in order to panic and get benefits. This way stress wouldn't be missinterpreted as a simple stat that you can spend to get bonuses, but a risky resource that you only should rely on in moments of despairing, life-or-death situations.