Beside the obvious jaws we see, cichlids (and some other fish) have an extra set of jaws in their throat (Pharyngeal jaws, very similar to the ones in the movie Alien).
Cichlids use these very unique jaws, compared to some other fish, that allow them to manipulate and masticate food as it moves (sometimes slowly) into the esophagus to the gut.
The double set of jaws allow them to process one food item, and still capture and hold another, or to slowly process a seemingly "too large" item.
Of course anything can choke, but just because it takes a while to process a large item, doesn't necessarily mean you need to go in and get it.
I had a Nandopsis tetracanthus swallow one of its brothers, about half its size, and take days to finally work it all down.
