If we were going to relate TV to computer in a simple way to understand is that where a computer is reading code to transform into the video signals we see, a TV would be much more like a "stream" device than that. It takes incoming signal that is essentially already processed and just puts it back together, on screen.
The SOC is more a product of the user interface and for the process behind things like reading off a USB, etc. On older TV you can "see" the effect of the less capable (chip) running the menus and such in a relation of time, and often the complexity of that UI.