Not sure the list really makes sense, though. It's 'big-ship' centric. Great as department heads, but when that's the entire department, doesn't really fit.
Generally makes sense as far as jobs to get done, but you gotta get that into SHIFTS, so you can actually run the ship 24/7. On a ship like that, they all have to be at least cross-trained in a couple things, so muddies the waters. With 14 people, probably don't need a Security Chief AND a Tactical Officer, for example. Wouldn't have a CMO AND a med tech, you'd just have the CMO and several people would have had med tech training (like Paris on Voyager, could pitch in when needed, but doesn't stand around there).
Need a couple people able to pilot, at a minimum. Even with 4 6-hour shifts, gotta have 2 so someone can always fly. You wouldn't have that many hanging around engineering, either. 1 to monitor and baby things, others would just come in to help in hairy situations. With such a small crew, you can't 'waste' spots like that. CO and XO trade off commanding the ship, 2 to fly, 2 to run engineering, 2 for tac/security, 2 of science, 1 doctor, and 3 trained specifically on whatever the mission profile is. Pretty much how i see it playing out.
Likely not more than just the CO and XO required to be an officer. Probably the doctor as well, as the additional training usually results in that. And the 3 mission specialists could have at least 1-2 officers in that crowd, depending.
In Trek reality, though, pretty much everyone was an officer, so really a moot point. But they could never really be consistent there, so easier to assume they've all been to the academy...
Tough to really pick who 'needs' to be an officer there. CO and XO, but on a ship that small, that could be it.