Video game is generally considered to be broader - people often refer to Quake as a video game, people never refer to Mario as a computer game. See for instance the [recent /. article] - it's never mentioned whether or not computer games are responsible for violence. Etymologically you'd be more correct, but people rarely worry about that sort of thing when they talk. Heck, note Zork and Ultima were already here.
The separation of the two is certainly canon, and I agree that it makes good sense for older games. The problem is that the distinction necessarily carries itself forward to the present, where it becomes a harmful anachronism. Games slip back and forth all the time, and Mario and Goldeneye pair up far better with Keen and Quake then which each other. Emulators make things even worse. This merging was brought about by the suggestion we be platform agnostic, and I can't say I disagree - there's plenty of room for separation when talking about genres or history. --JG
But how to pigeonhole games by genre? There are so many examples of series that span many genre's and styles, that appear at first glance to be one thing, but are in fact another. Take for example the Tomb Raider entry, the fact that the first 3 instalments are 3d doesn't make it a 3d series, "huh?!?" there is a 2d Game Boy Color Tomb Raider. But that's just the beginning. A better example again is [Panzer Dragoon]?, the first two games were on the rail shooters, the third, Panzer Dragoon Saga was an RPG. Best yet is Super Mario; 2d [platform game]?? or 3d platform game? or kart racing game? or all three and then some more.
I haven't the answer, perhaps games that aren't so readily defined should he left just that, undefined. --Neeklamy