I would argue the linguistic definitions as well as the political definitions are important. Often these form part of the national or cultural memes about how we define ourselves.
Also the definitions add legitimacy to ‘legal’ as to ‘illegal’ armed conflict – for example no one would try to legally argue that crew of a Sherman tank killed when it was hit in Normandy in 1944 were murdered compared to those RMP lads who were killed in that Iraqi police station a few years back.
Please note that I am not saying what is ‘right’ in the moral sense but it is important that these definitions are understood else (legally, politically, linguistically) else the next time you argue over your parking space with your neighbour… you get my drift.