You can watch any in-home channel on your phone, tablet, or laptop with Xfinity Stream while on your home WiFi; it's like having an additional set-top box. (Comcast has the right to deliver the same channels and OnDemand content that's available on your X1 box as long as you're in your home and on the Comcast managed network.) However, the rights for out-of-home viewing are different—and negotiated separately—and in the case of the NFL, they're even weirder than usual. For example, in past years—and I think this is still the case—even though ESPN is available as both an in-home and a TV Go channel in Xfinity Stream, you can't watch Monday Night Football on the ESPN TV Go channel via the Stream app on a mobile phone unless Verizon is your cellular carrier. This is because the NFL made a deal with Verizon to be the exclusive carrier of its games on mobile phones. (The deal did not apply to tablets.) If you Google "nfl mobile viewing," there are a few good articles that attempt to explain all the ways you can watch NFL games on mobile devices, but you'll notice phrases like "not every game," or "not every device," or "except for games broadcast on [X network]" because of the crazy patchwork of deals between cable/satellite/cellular/streaming service providers, networks, and the NFL.
I'm not sure that helps very much, sadly. In-home vs. out-of-home viewing rights are hard enough to explain on their own, but throw in an a professional sports league, and it gets even harder. :-)