A lot of people think that on this site (that people downvote others for competition) but I don't think it's likely.
The reason why I don't think that is because I've advanced really quickly up the top 100 leaderboard. If people in those slots were jealous for their points, or were using alts to downvote others and keep their memes high, I would have been a target. But so far, I haven't been subjected to any downvotes in any systematic way.
So although I do see people getting in flame wars with each other occasionally, and downvoting for that reason, I really don't think it's common practice on imgflip for people to downvote each other for competition.