We're not talking about MS going into making dumb set-top boxes and competing with the Chinese no-brand devices. There's little money to be made there. But by including media functionality, MS add important value to their device. If MS were to just release a console with no media functions, people are going to have to make a choice between it, a set-top box, both at added cost and more boxes in the living room, or a rival device that does everything (Sony or Apple, say). Those with internet TVs, maybe 5% now and maybe 25-35% in 5 years, may be happy to just get a games console that can do nothing else, but they are far too small a market to aim for.
It's basically essential to support media functions. Thankfully it's also cheap, adding next to nothing to the console cost, so it basically comes free. It doesn't detract anything from the game experience, and can even augment it when you can multitask (custom playlists, or jump to a browser in game).