But that isn't 'The whole room is your "desktop".' If you are restricted to having your desk in front of you, you might as well be looking at virtual screen(s) on your desk.
I had not seen the Glove80 before, it does look pretty nice. Though I would prefer a bit smaller. I don't really use F keys, and use layers for things like arrow keys.
Glove80 has hot-swappable tripod mounts, so I attach it to my chair, or I use clamps to attach it to a table, or to short tripods standing on the floor, or to very tiny tripods that can give the keyboards an extreme near-vertical angle on a desktop. Very easy to get an ergo setup going when traveling this way.