Um, Android and iOS are mobile platforms. And Microsoft's ongoing development for apps on those platforms does indeed demonstrate their commitment to mobile. Their commitment to mobile didn't happen on your terms, but its very hard to deny. They're developing mobile software at a breakneck pace.
But back to the main point of the article, Microsoft's Movies and TV has one thing going for it that Groove didn't: an audience. The Xbox is the sole entertainment console attached to many people's TV, and with more people cutting the cord, MS Movies and TV is uniquely positioned to be a sole provider for digital content in a way that Groove wasn't. Most music streaming is done on people's phones, and Groove didn't have a built-in fan base since nobody owns Windows Phones. A service like Groove will never be able to break into such a saturated market without a strong mobile ecosystem, but the Xbox's strong living room presence might be enough to keep their Movies and TV service afloat.