Could it have simply been adopted from the Germans and their Kampfeinsitzer?

Good find Louvert (I should have looked into Flight magazine achives better in the fist place myself...). By September 1917 the term "Fighter" seems to be already used in its modern meaning of single-seat Airco D.H.2 (?). That leaves the question, did the term spread from military to civilian use or vice versa .

@Fullofit, At least to me it seems pretty unlikely that the British would have purposely taken and translated a German term in middle of WW1. In both languages calling a machine made for fighting a fighting machine is pretty intuitive and I'd imagine both terms came up independently. Especially the term "Fighter" doesn't translate from the German word either: Direct translation of Kampfeinsitzer is closer to "Combat-single-seater".