It might be relevant that the original post talked about creating work specifically for an "Alternative Comics" contest. If the contest is only for alternative comics, then "is my comic an alternative comic" is a relevant question!
But looking at these replies, it seems there's not a really solid definition? It's just, something outside the norm -- everyone has a different idea of exactly what that is. So the American comic book shops are going to define anything that isn't aimed to their core demographic as outside the norm and "alternative," while people on Tapastic aren't going to see that work as being outside the norm, and instead point to Xerox'd, stapled comics about dark and not-often-explored themes.
But today, when it's so easy to get a semi-professional-looking comic printed through a place Ka-blam, does Xeroxing your comics really mean anything.... other than that you want to look "alternative?" Once upon a time, the people photo-copying their pages were the ones who didn't have a chance with a publisher, so it was a sign of something weird and different. Now that independent creators can get professionally printed work, it's only really indicative of an aesthetic, or a lack of a desire to fit in with professionally printed work. That seems like a weirdly arbitrary line today.
As far as whether or not you can or should enter these sorts of contests, I think you could go either way. There's no reason you can't -- there's no solid definition of "alternative," and you could certainly argue that your comic's themes fit under that wide umbrella of "outside the norm." But at the same time, I can understand not doing it if you feel disingenuous being there. I used to joke that my journal comic is "not indie enough" for some indie comic conventions, because, even though I do an auto-bio comic, I get it professionally printed, and "indie" carries this connotation of "rawness" that I don't really value in my own work. I could certainly put my work there and no one would question that it has a place there, but it would be unlikely to resonate with that crowd.
So, no reason you can't enter! But if your comic isn't the sort of "alternative" they're looking for, you may be unlikely to win! I don't think that means you can't enter if you wanna try, though.