I’m not familiar with Forbidden Desert, but I’d personally advise against a game like Castle Panic. I’ve played tabletop games with one player remote, viewing the table through a webcam, and the biggest issue was always the one remote player literally lacking perspective - we constantly had to adjust the webcam to give him a better view, and it was still difficult for him to keep track of positions (and he was a veteran wargamer for whom tracking tabletop positions was second nature). For a game like Castle Panic, which literally has a lot of moving parts, I’d think it would be almost impossible for the remote player to have a sense of the board.
One game that comes to mind is Cartographers. I don’t particularly care for it, but that’s because it’s just not my kind of game. The rest of my gaming group loves it. The big advantage is that the remote player would just need a copy of the map pad, and a webcam focused on the common cards. Everyone basically plays their own mini-game on their map pad based on the common cards - there’s no real player interaction other than table chat and comparing point totals, and showing off your map at the end (which, again, webcam should suffice).
I think there are other Eurogames in that design space, where the players have minimal interaction, but those often involve common physical resources that need to be passed around. There may be other games like Cartographers where you just need a commonly viewed reference that would work as well, but that’s not a game design space I’m very familiar with.
There are also social deduction games (another game space I don’t particularly care for and thus am not terribly familiar with) that would probably work fairly well with a remote player on a webcam. For example, as long as everyone stays in-frame, I don’t see why One Night Werewolf or a similar game shouldn’t work with one player remote.
If you’re open to an RPG other than D&D, a system that’s designed for “theater of the mind”, like FATE, GUMSHOE, or Powered by the Apocalypse could be a fun option, with a webcam on each end so you can all see each other and have something approaching normal table interactions.
More ambitiously, I’ve seen groups using a flatscreen turned on its back displaying a Roll20 or Fantasy Grounds map. If you go that route, everyone in-person could sit around the “table”, sharing that one screen, while your remote player logs into R20/FG and uses it the normal way.