The interest of real Gatling guns are for cooling purposes, to avoid overheating a single cannon. But those guns mostly cool down thanks to the ambient air, which is conspicuously absent in space.
In space, you have to use radiation to cool down, and this is dependent on the surface that can radiate away from the ship (hence why real spacecraft have big radiators, comparable in size with solar panels).
It would make more sense for the guns to have, for example, a few radiator fins running its length, or a cooling system plugged in the general ship cooling system - maybe more efficient, but also more complex and prone to failure (like when a piece of shrapnel is sticking out of your cooling pipe).
All in all, Gatling guns in space are inefficient and needlessly complex compared to other system (and the rotation means they are harder to aim around very fast due to gyroscopic inertia, but that's probably a minor problem).
You could maybe justify them for with some engineering reason, but that's probably not the kind of guns we will see in space - if we ever see real slug-throwing guns again in space at all.
Then again, 'maybe justify them' is good enough to me, because they look pretty badass.
And if we go that way, the lack of radiators and visible fuel tanks await...
It's the exact same in the book, and while I had a similar reaction, it actually works quite well - would be a surprise if it doesn't in the show.
Only minor problem I have with the show so far is that they still fall back to this tired old "torture is acceptable to gain information" trope, even through a public organization went to great lengths to test this myth in the name of Science, and prove that it is absolutely, utterly inefficient when used that way.
Come on, people, it is a tool for terror, not information gain! You have fancy futuristic truth serums and mind scanners for that (you do, don't you?) At least use it properly, not hidden in counter-productively black sites...
On the other hand, that one scene was an effective way to show the difference in physiology between Earthers and Belters.