'for' is heavily overloaded as an English preposition. You are expecting a connotation of "for [the benefit of] Linux" versus the connotation of "for [the purpose of] Linux". Another example in English might be the relative meanings of 'for' in "this gift is for you" versus "this gift is for good behavior".

Other languages use multiple words or different cases for some of these situations. English leaves it ambiguous.

it's the subsystem for running Linux. It's not actually Linux, and after enabling the subsystem you still have to actually get the Ubutntu image. That image is the Linux part.