So I don't have cable. I have a smart TV which has built in apps (Hulu, Netflix, HBOGo, Pandora, YouTube). My TV has an ethernet port and I get all my content fed through the Internet, into my TV and through the app's interfaces without having to pay for TV.
I can do this because I have a newer TV built for this. For those that don't, the exact same services can be achieved through Roku, Google TV, Apple TV, et al. I don't know about this Chromebox...
If the NFL were to liscense an app for my TV (like the MLB does), I could then watch football games the same way.
Another way to achieve this: I also have a Mac Mini (just a desktop computer) hooked up via HDMI to my TV, so anything that can be streamed through a web browser I can watch, too. This creates redundancy with most of the apps 'built' into my TV, but comes in handy for some Hulu content that is web only (MST3K), services like preseason live, et al.