This is fun, and there are little pokes at the comic book fandom. Still, it's not half as clever as most parodies, or anything breaking the fourth wall, partly because it's not as self-aware. These are just meant to be fun, whereas most parodies really play with the tropes, most times pointing out the flaws within said tropes. Likewise, breaking the fourth wall is more effective when it has teeth: commenting on things that are harmful, or simply not well done.
Grumpy Cat aims to be harmless fun, and it is that. But it comes off at toothless: generic humor that doesn't really make a point except that, say, Superman vs. Batman was lame. (Which is so almost universally agreed upon that even if it has a little teeth, it's little enough to feel toothless: it's okay, because it knows it won't upset most of the comics fandom.)
And this isn't a bad thing. It was fun enough for that harmlessness. It was amusing. I just didn't feel as strongly about it as something that wasn't afraid to go for the jugular: that safety net made me feel like this was too strongly neutral about almost everything. And I wanted to feel something about this. It didn't have to get super intellectual, but something more clever wouldn't hurt. (I like plenty of things that are good, harmless fun. They do tend to have some sort of excellence about them, though: the writing, the ideas, the art, the execution, something. This felt fairly average on top of not really wanting to hurt anything, even if it meant not really saying anything, and that made me like this a little less than those other good, harmless fun things that I've read.)