When you “add a game” to the steam library, you’re just creating a link to another file on your system, not really shifting the management of it over to steam (so no updates or the like), and if you logged in on another machine you wouldn’t be able to download the game through steam.

more importantly you can’t take a steam game and move over your license to use it, or ability to install/update it to some other platform. If you decided you never wanted to use steam again, that you liked some other platform better, you would still have to use steam to access those games.