It's good for Microsoft but not necessarily the Xbox division though. Xbox loses the massive competitive advantage of Azure when it comes to streaming.
Should they keep pursuing their own hardware, then they can always find ways to make sure their own hardware benefits more ... If it becomes a success, it just means that Sony now depends on Microsoft and if Sony does well, so does Microsoft. So not a bad position for them to be in.
This partnership may well not amount to much if Google Stadia fails (wouldn't be the first Google balloon to deflate and fall back to earth, after all). But if it does, I'm wondering if they'll ever release hardware, they'll just keep the Playstation brand (I would).
However, it's fun to make up names. Inspired by a Eurogamerthread, my current favorite and own suggestion would be
PlayBox S 3XY Pro