This is the source of the confusion. USB is not HDMI. I doubt there is any way to use a USB port to hook to a tv. You can hook up things like roku or a memory stick but I have never seen a tv that supports hooking up a router. The USB port on a router in most cases is only used to hook up stuff like hard drives or in some cases they support cell modems.
In any case if you want to hook a tv up with a cable a ethernet cable is going to be a lot faster than any USB port and is simpler since USB is not really designed to carry network data.
The coax connector on the TV I suspect is only for cable tv channels. it likely does not carry data. Technically it is possible but I don't think your tv or your router has support for...