I know almost no Japanese, but while watching fansubs of the HnG manga, certain japanese words stuck out as being obvious loanwords from English, like "internet". But one thing that surprised me: it sounds an awful lot like "rival" is also borrowed from english. I could be mishearing, but it sounded like every time the translation said "rival", the character said "rival" (or "raivaru"?) If I'm right about this, is there not a japanese word that means rival? Maybe the english word just sounds very similar to the japanese?
I know no Japanese, but according to this Wikipedia page, ライバル (raibaru) is what you are looking for.