As far as the Rambam is concerned, there are two very obvious reasons why he chose to write neherag rather than meis. The more famous one is that he is referring to the actual case of Bar Kochba, who was killed. Everybody knows that the derech of the Rambam is not to be mechadeish dinim but to stick as closely as possible to the words of Chazal. The other (and to my aniyus daas more likely) explanation is that the Rambam understands locheim milchamos Hashem kipshuto, that Moshiach will be engaged in fighting actual, physical wars. As such one who is not truly Moshiach will likely end up neherag, rather than simply meis.
And to Shlucha’s assertion that no one bothered to be medayeik in the loshon hoRambam before Gimmel Tammuz because “it wasn’t necessary” – are you kidding?! Almost eight centuries of talmidei chachomim horeving on every kutzoh shel yud of the Rambam, including the entire seforim that are not practically relevant today, and nobody noticed this diyuk because it wasn’t necessary? Come on!