Even if they weren't officially a couple, that's on the same level with cheating on her.
... that's just the same as cheating on her.
付き合っている = dating, in a relationship, (be) a couple, involved with, (be) boyfriend and girlfriend
この文脈では、「officially」（公式に）の意味は「二人で決まった」「正式に」「formally」です。
アメリカ合衆国 
フィリピン 
