The upvote/downvotes system does provide one other useful function currently:
Identifying correct/incorrect information.
For example, let's say you're new. If you make a thread asking "Do Riven's spells benefit from life steal or spell vamp?", you're going to get both correct and incorrect responses. The vote system will distinguish them.
I used that example, because that sort of thread happens periodically on GD, and you can see this exact thing play out. You get people saying "Spell Vamp" with upvotes, and some people saying "Life Steal" with downvotes. The votes serve as a way for people who know what's actually going on (luckily, they are the majority on the forums it seems) to weigh in without bloating the thread.