the player is probably concentrating on the continental battles and/or on players with impressive defense armies, which can easily be worth thousands of points per battle. if other players in the neighbourhood are focussing on PvP against players who don't have very much in their defense armies, their scores would be lower. battles against big/advanced armies give you more points than battles against smaller/less advanced ones.
but if you feel someone is cheating the proper way to report it is through an in-game support ticket, not here in the public forum. to file an in-game ticket, right-click anywhere on your main village screen, choose "support" from the pop-up menu and then follow the cues from there. "breach of rules" would be the appropriate choice when you define what type of ticket you want to submit.
Depending on what he's fighting, I don't see why it isn't. In my EMA tower I currently have 16138 points in 7 battles, so an average of 2305 points per battle. And I probably could have gotten even more since I think I'd still be winning if I ditched the two EMA troops and went with only the Iron Age troops.