My take is people are sloppy with words. So in the 1970s when we had ATARI console games, like pong, they were called video games. We had large quarter driven consoles, like PACMAN, and they were called video games, and in the late seventies we had personal computers like the TRS and Apple //, and they were called computer games, though I guarantee that people called them video games too. Regardless, they are all computer driven games. Of course it may vary from country to country, and most importantly, I may be completely wrong. I'm just recalling what was what at the time. In the '70s, I did not have an ATARI, although my brother in law did.
I appreciate the question. There are times I get fixated with the idea that what we see on YouTube are not "videos" because I come from a background where videos were associated with tape and YouTube has digitally recorded images stored on a huge array of hard drives. However, words evolve and I've accepted that YouTube has "videos," even if I personally refer to them as recordings.
This is what Wikipedia has to say about Video. It goes one step further, stating that originally video was reserved for live television transmissions.
I still type e-mail, not "email" because there was mail, and then we had electronic mail, or e-mail. Someone got really fed up with me once when I tried to explain why I thought e-mail was more correct. I really don't care anymore, even if I still type "e-mail."
(I know, this is all rambling...)