It's a floating platform. Same as the ones SpaceX lands its rockets on. Same as a gunboat firing projectiles.
Will a launching rocket impart force to the platform? Yes. But unless the platform is super weirdly balanced, or the rocket absurdly oversized for the platform, it will stabilise after rocking a bit. (You'd have to design the platform to be stable in winds, anyway.)
And if you do have an absurdly oversided rocket, you don't launch it from your platform. You float it off to the side on a dedicated launch "boat" and have it ditch its floaty as an ultra-early first stage.