Something must be up with the steam protocol registries not executing the needed commands. Check this in regedit
HKEY_CLASSES_ROOT\steam\Shell\Open\Command
Should be "path_to_steam.exe" -- "%1"
Thats actually kinda cool, you have portable yet volatile storage lmao. But indeed that is completely unreliable as a storage medium so I'd keep it for fun and just get a new flash drive.