I can't comment on whether the application process does require a windows version, why would you cut out 95% of the customers by not having one? See http://store.steampowered.com/hwsurvey for the stats.

You should notice that the full line there is "Your game must be able to run on Windows as a stand-alone application" which I took to mean that you (the developer) must package all the dependencies with your game. Steam would take the reputation hit if it distributed software like Linux does (dependency hell).

Seems especially odd since SteamOS is a thing.