I think the problem is that we don't have a good enough terminology for all the different kinds of devices out there. For instance, I could argue that Simon fits your definition, because it does "generate its own display" which consists of LEDs or flashing lights or what have you. Plus, what about the various "videogames for the blind," which don't generate video but do output sound? Also, are we going to count Lite Brite because it has a display? Etch-a-sketch?

I think the word "video" is the problem with "videogames," but what else can we use? We've already noticed the problem with raster/vector etc. "Electronic games" doesn't seem to work, neither does "computer" or "console" games, since that distinction is really fuzzy anyway. If you just flat out call them "games," then you really open it up.

Whatever word we come up with, it ought to cover everything from Tennis for Two all the way up to Spore, and exclude stuff like Simon, Electronic Battleship, videopoker machines, etc. What we need is something besides "video" there, but I honestly don't know what. We may just have to come up with a new word and use that instead. I mean, can you imagine trying to talk about Velcro or Post-it Notes without using those words, but insisting that you only use existing words?