Captain Buynovsky is a lot like Captain von Trapp from The Sound of Music. No, really. They're both naval captains; they're both super strict and lack sense of humor; they both boss others around; and they both have a tendency to fall in love with nuns and to randomly burst into song. OK, that last one doesn't apply here, but Captain Buynovsky does have things in common with Captain von Trapp at the beginning of the movie, before he loosened up and got in on his family's musical/variety acts.
See, both Buynovsky and Captain von Trapp are largely disconnected from reality when we first meet them. Both of them act like they're still commanding a ship and neither of them adapt appropriately to their current situations. We can see Buynovsky's lack of adaptation in two major ways: the way he speaks to people and his physical appearance.
The captain yanked him up by the scruff of the neck and gave him a push in the direction of the handbarrow.
"Go and fetch sand, you feeble bastard!"
The captain saw no difference between work in a camp and work on shipboard. Orders were orders! He'd gotten very haggard in the last month, the captain had, but he was still a willing horse. (345-347)
Buynovsky isn't differentiating between his former life as a naval captain and his current life as a zek. He goes around barking orders and insults at people, and he uses up too much energy during the day. He hasn't yet learned that the world of the camp operates on a very different set of rules to which he has to adapt.
Now he was behaving like those he had tried to drive away with his metallic voice five minutes ago - taking up space to which he was not entitled [....] Moments like this [...] were very important to him: they were turning the loud and domineering naval officer into a slow-moving and circumspect zek [....] (467)
Shortly after this the captain gets some extra gruel and is thrilled; but at least Oliver Twist had the sense to ask for more. Buynovsky hasn't yet learned how to take care of himself as a zek. And this is what makes him such an important character in the book.
As the new guy in camp, we get Buynovsky's struggles and how difficult it is for a person to adjust to life in prison. Buynovsky is slowly changing into a capable zek, but he isn't doing it fast enough. At the end of the book, he's taken off for a stint in the punishment jail for back-talking a guard. The poor captain may very well be doomed, and in a way his character acts as a powerful damnation of the whole gulag system. The gulag system takes the captain's life in more ways than one: it degrades and humiliates the proud and intelligent captain, and it may also end up killing him.