They don’t care if you play on steamOS, Windows, or a steam powered adding machine.

i think yes and no: they make their money from selling games, so they want more people to buy more games from them

… but, SteamOS achieves that in a multi-faceted way:

• it provides a fit-for-purpose platform for handhelds and consoles which previously steam didn’t have any market share over, and if that’s in SteamOS they have a massive advantage
• it gives valve some leverage over microsoft (if MS controls the platform that you depend on, they can do some pretty wild things and you have no recourse). in this case, they definitely care about bumping their numbers - more on SteamOS means less power microsoft has over them
• it creates competition, which forces microsoft to invest in making their own experience better, and better experience anywhere means probably more people game more often

i think that last point in particular is critical: every $ valve spends on steamos is multiplied, because microsoft has to spend their own money to keep up, and it propels the whole ecosystem forward