If this version of M'Benga needs to be crammed into the old continuity, then, whatever his position, he obviously left the Enterprise if he is the CMO in SNW. Piper is identified as a department head in "Where No Man...", McCoy is clearly the CMO in the two episodes M'Benga appears in. It is noted in "A Private Little War" that M'Benga spent time on Vulcan, prior to when we see him in TOS.
We have to age him up a bit for SNW, as Booker Bradshaw was only 27 in TOS, but it could be simply that M'Benga wasn't interested in being a starship CMO after giving it a whirl. He returned to the Enterprise under McCoy to finish his commitment to Starfleet in 2267-68.