I have a Samsung Galaxy Tab® 4 (10.1) with LTE service through Verizon and I have definitely not been able to watch NFL mobile on this tablet, even though I paid extra for the NFL mobile service on my account. It should be accessible to all devices on my account, or at the very least, I should be able to pay an extra fee per device to have it work on more than one device. It makes absolutely no sense that there should be a restriction on licensing the app to a smart phone, and specifically not to a tablet.
The agreement with NFL and Verizon Wireless is for the phones only. NFL has the agreement with the cable companies for the larger devices like tablets.