We have the same thing. Our bath is a wet bath -- toilet inside the shower area. So I always wipe down the vinyl wallpaper with a squeegee, followed by a towel. The towel dries overnight, and we can use it again the next day.
Bottom line -- no problem. We spend weeks at a time with this setup, showering every evening.
I tried waxing the vinyl wallpaper with car wax -- it accomplished nothing and I stopped doing it.
We have a vinyl shower curtain that hangs inside the door. But there is no curtain protecting the wallpaper.
I am not sure that the wallpaper really needs to be wiped down every night -- but it can't hurt, right?