Absolutely not. Pictures don't need to be pretty. Music doesn't need to be catchy. Dance doesn't need to be graceful. To force an adjective on an entire artistic medium is short-sighted and overly reductionist at best, and damaging for anyone working in that medium at worst. Suddenly the onus on someone trying to express himself in song is to not only bare his soul but to make sure there's a beat you can dance to. The painter can't just pour his inner demons out on the canvas, but must do so in a way that is palatable to the eye. The dancer is no longer able to use their body to its fullest expressive extent because loose, sudden, or jerky movements are seen as a lack of skill rather than a conscious effort.
To clarify - the OP makes it pretty clear he's not talking about "engaging" or "interesting" as valid interpretations of fun - just explicitly
fun fun. "Whee, I'm having a great time on this waterslide!" fun, not "Watching Schindler's List is grippingly powerful entertainment" fun. No one is arguing that games should be skull-crushingly dull (well, maybe Ian Bogost, but I digress). Seriously, if games are required to make you feel the same way a 10 year old boy in the middle of a neighborhood waterwar feels, and the need to generate that silly emotion supersedes
any other thing you're trying to do with your work then it's no wonder we have a medium riddled with nothing but male power fantasies and simple toys.
I mean, look at these games. They've been covered before and many of you have already seen them, but they're engaging without necessarily making you feel like you're a six year old at Disneyland:
Every Day The Same Dream
Real Lives
The Passage
Some of these games might not be to your tastes, and that's totally cool. But there's a difference between games not one being to one's liking and the requirement that all games conform to a single aesthetic. Games like these, and numerous others, prove that you can have an engaging experience that isn't necessarily something you'd invite your friends over and split a few beers while playing on a big-screen TV.