You don't have to find it enjoyable personally, but it has to try to be enjoyable. Some aspect of the game has to be fun to some people.
What gives you the right to say what games should and should not have?
The dictionary, under the definition of the word "game".
Don't misinterpret any of this as saying that I think certain games have more merits than others, because I don't. I just use the more literal translation of the word "game".
My apologies then.

(Also for sounding rude)
But I don't agree with the idea that it has to fun for it to be a video game. If the only thing that differs between it and a "regular" game is the intention of the developer(s) (they don't aim to make it fun), then what is it?
When we're talking about videogames, I'd say the most fitting one is:
[2.]a. A competitive activity or sport in which players contend with each other according to a set of rules: the game of basketball; the game of gin rummy.
I don't think that really fits at all. There are many single player games and games that aren't played to be competitive, but moreso played for enjoyment (RPG's, say, aren't competitive).