Those are valid concerns, but I don't see any reason to believe that a hybrid approach for handling the two ecosystem couldn't be possible. As mentioned by their discord posts, their patches to the game are directly parsed by CodeWeavers, and options for server-sided anticheat or a Valve-style "Trust Factor" are both on the table.
I could also see this being beneficial regardless of the eventualities because of the barrier of entry - novice or less tech savvy users who wish to remain on the Windows platform and desire to cheat could be more deterred (or caught) by the kernel level anticheat. On the other side of the aisle, linux users could be targeted with a Trust Factor or higher level of User-space scrutiny, given a lower likelihood for running an excessive amount of background processes (compared to Windows).
They did say and/or steamdeck, and specifically called out Wine and Proton, so I presume the changes are OS agnostic. It's just the steamdeck has become synonymous with Linux gaming in the public eye.