how useful is a torque dampener that you install on your engine to reduce engine movement?

The damper isn't the best option. Stiffer, aftermarket polyurethane mounts will make a big reduction in engine movement.

but i mean, will there be a significant gain to my engine not moving as much? this is only a dx with 105 horsepoer, and primarily i wanted to put it in so i dont feel the chassis vibrate because of the engine, but ill also do it if there are significant gains that ill see.

there is no gains with aftermarket motor mounts. if your motor mounts are torn, on a dx, it is pointless. search what the purpose of stiffer mounts do ;)

stiffer mounts and inserts will create more vibration throughout your car. Since the mounts aren't taking the grunt of the vibrations, they have to go elsewhere.

I've only seen one car using a torque dampener and it was a drift car. If you're looking to lessen the vibration you feel, I would redo your sound deadening with some heavier stuff. It'll keep the road noise down and should cut down on some of the vibration you feel.