Rifleman does seem to boost them. when I put points into single shot rifle damage my double barrel shotgun gained it too.
One of the loading screens specifically says shotguns fall under rifleman.
Early on I got an assassin's double barrel shotgun from a legendary rad roach. It does double damage to humans. I kept modding the damage, range, and recoil every time my gun nut level would allow it. So, I kept a pretty good watch on which weapons did what damage and when I took the riflemen perk it did jump. One shot raider in the head is so much fun. I'm trying to get good at catching the eyeballs from the aftermath in midair. Practice, practice, practice.
Yep, Rifleman covers shotguns too. I have a Gun Nut at 3/4 and Rifleman at 4/5 and my shotgun does almost 150 damage. That said, I sort of wish shotguns had their own perk, Shotgun Surgeon, and it was nested in the END tree. That would help spread out the weapon love a bit and open the opportunity to give shotguns their own flavor (although the armor ignore is still awesome).
Useful to know. This would make a Rifle/Shotgun build to be the "cheapest" as shotgun can take care of close quarters while Rifle touches them from a distance without having to blow extra points on 2 or more perks for 2 different types of weapons. Pistols get more shots in VATS though. I don't think I'd ever waste points on automatic or heavy weapons personally.
Non-auto shotguns - Rifleman
Auto shotguns - Commando
Before you spend a point make sure you have the correct mod on your shotgun and check your damage on pipboy. Add a point and then check your damage again. I have a non-auto shotgun build and the Rifleman perk does increase its damage. If you have an auto shotgun you will need to put points into Commando.