Mechanical watches have shock absorbers but impacts should be avoided if possible. Here's an article that helps explain mechanical watch maintenance. https://gearpatrol.com/2018/11/20/mechanical-watch-maintenance-guide/
FWIW I wear my mechanical watch while shooting and sometimes it takes impacts from daily wear. I treat my watch like I treat my truck. Both are not delicate and can take use and some hard use, but they are machines with moving parts and their repair can be costly.
My question was do you have any first hand instances of a mechanical watch damaged by shooting?