You don't even have to look at the remake as any kind of romance per se, it can just be looked at as an innocent flirtation with romance, children practicing for the later serious romances they will encounter in life. So, you look at it as a friendship really. And kids can get just as jealous over that kind of thing.
edit: and as far as the arc goes, it has been a while since i saw the original, but if memory serves, it is the same kind of deal, a backdrop to the main plot of the movie, which is about the bullying and standing up for yourself. So, it doesn't really need to go anywhere.
What the remake is very good at though, is exploring the fear that accompanies a child who is bullied by kids who outnumber and are physically stronger than them, who they are forced to encounter at school.
That fear and sense of dread was much more palatable in the remake than the original I felt. It was scarier because little kids are generally more out of control than adult teens, and theses kids carried the same devastating physical prowess as an adult. It was like watching adults with the minds of children bullying a child.
So, in that sense it was much more successful in making you fearful for the protagonist.