Correct. Unfortunately, it’s something that each desktop environment or window manager has to implement themselves. But all the button is doing is moving some config files around, so you can probably do some digging to figure out what it’s copying to where.
Honestly, it’s probably not worth the hassle to try to install system apps elsewhere. Steam and Lutris, on the other hand, can put games on any mounted drive. Install them as normal, and then in Steam, set up a steam library in
/Apps
. In Lutris, you should have the option to choose where each game is installed each time you install one.