I would agree with Skorpyo, that the "meaninglessness" of the Grind depends on the ultimate outcomes - and the number of possible outcomes. Grinding in World of Warcrap for example has a very limited set of outcomes, and feels more like the greek fable of pushing Sisyphus' stone. While Minecraft has a seriously unlimited amount of possible outcomes for the grind.
But for the sake of argument, I'll assume the OP was referring to "meaningless" grind, such as World of Warcrap, EVE, Star Wars Galaxies, etc.
This depends on the psychological predispositions of the individual asked.
I suspect the people who enjoy meaningless grind may be...
1)Those who find repetition comforting. A lot of people have varying degrees of Obsessive Compulsive Disorder (OCD) - but not being a problem for that person, it won't be diagnosed. A friend of mine is OCD about high-scores. He has to find every little item that exists in the game world. Or has to be #1 in any number of obscure games. His little brother has Aspergers Syndrome.
2)Boring people. Because they have so little love for life and for a good challenge, that they would rather play it "safe" and do some pointless repetitive task. These people have low self-esteem.
3)Stupid people. They don't realize that it's "boring", because their brains are working overtime for the simple task they are presented with. It's "fun" to them.