As you may have suspected, the term alligatoring does come from that prehistoric, four-legged creature, the alligator. The term is used for cracks that form in paint when it dries that resemble the pattern of an alligator's scales. (Take a look at an example of alligatoringfrom the Fine Arts Conservancy.)
The term alligatoring is used by some people as a synonym for craquelure; others distinguish between the two, using craquelure for finer cracks associated with ageing, when the paint shrinks and becomes more brittle.