My understanding of it is that Google are exercising item 8 in their terms of service:
Usage and Quotas. YouTube may, in its sole discretion, set a quota of operations on Your YouTube API usage. You shall not attempt to circumvent automated use-quota restrictions.
Now, since the total number of people using Windows Phone's YouTube API key is pretty large, a restriction on this effectively disables the app.
Unfortunately Microsoft isn't able to get around this legally because of other restrictions in the terms:
Your API Client will not, and You will not encourage or create functionality for Your users or other third parties to:
...misrepresent your identity when registering for use of the YouTube API, use the developer credentials licensed to a different individual or entity, or mask Your usage of the YouTube API
A consequence of these two rules is that Google can (and presumably has chosen to, if Microsoft are to be believed) block Microsoft's YouTube app from properly working, and although other developers on other platforms are not affected, and Microsoft would be able to technically work around the restrictions (e.g. by registering lots of API keys), doing so would be in violation of the terms and conditions of the YouTube player - and hence would put Microsoft in a bad legal position if they released their "working" YouTube player.
It does seem to me that companies should provide the same service to all users of any given API. If Microsoft started playing tit-for-tat by doing shenanigans like saying "HeapAlloc returns NULL always if the process is called 'chrome.exe'" the world would be a worse place.
Other than when a court order instructs you otherwise, you shouldn't have any logic anywhere in your app that treats some customers as different to other ones.