Launching the desktop file without modifying anything works as normal. I should report this itch client bug to the developers of the itch client.
Thank you bringing this to my attention! Rex was made before itch had a client (I've not even used it yet myself), so I have no idea how it plays with it. I'm glad you managed to get the game working, and I'll see if it's anything I can fix on my end as well.
No problem! By the way, I opened an issue on the itch client project and they took notice. The issue's page by the way: https://github.com/itchio/itch/issues/2436.