^Engine dampers are basically little shocks that mount from the top of the engine to the chassis, keeping the engine from moving as much when you drive. Kinda like an extra motor mount. Supposedly gives you better engine response and takes some of the stress off of the motor/tranny mounts and tranny.
And to the OP, every one of the engine damper kits that I've ever seen are application specific, mostly because the mounting brackets. Are you sure the one you have will fit integras? You could always make some custom mounts too.