I think you are right, this is the best definition.I would categorize small pets the following way:
Common Rodents: Hamsters, Gerbils, Mice, Rats
Exotic Rodents: Chinchillas, Degus, Prairie Dogs, Squirrels (any species)
Common and Exotic Non-rodents, on the other hand, are harder to define. I have ferrets and rabbits, neither of which are rodents. Other non-rodent small pets include hedgehogs and sugar gliders.