It looks very much like "Felodon" is made up of "Feline" and "teeth" in a bit of a Linnean pidgin construction.
The Linnean binomial naming convention is to construct a name using classical languages which is a bit descriptive of a new species. The original idea -- invented back in the days when any educated person was literate in at least one classical language -- was that the components would always be from the same language. E.g., "Tyrannosaur" is derived from the Greek for "tyrant" (τύραννο == týrannos) and lizard (ςσαύρα == sávra).
(Today, this is pretty much ignored because (a) how many biologists know Classical Greek and (b) how many care that they are mixing Latin and Greek in one coined word and (c) a lot of the obvious coinages are already in use.)
So Felodon is pretty clearly Felo+don, and don is a very common bit of species names from the Greek δόντι (== dónti) for "tooth". E.g., Mastodon, Smilodon, etc. It might also be from Latin where 'tooth' is dente (gotta love Indo-European!). This would ameliorate the faux-pas of mixing Latin and Greek.
Felo does not have an obvious Greek source, but seems likely to be from Latin "Felis" which is the source of our "Feline": cat-like.
Felodon is described as somewhat catlike:
It was of moderate size as carnivores went—some four feet long without the tail—and looked rather harmless as long as it kept its mouth shut. It was lying in the center of the cage, so it was difficult to judge the length of its legs. It showed no trace of the tendency displayed by many captive animals, of lying against a wall or in a corner when relaxed; and there was none of the restless pacing so characteristic of Earth's big cats under similar circumstances. It simply lay and stared back at Lampert, so steadily that he never was sure whether or not the cold eyes were provided with lids.
So in spite of it also being described as somewhat reptilian and somewhat amphibian, it seems like seeing it as cat-like is not unreasonable.
And I'd note that the picture illustrating to story (which can be found in the OP's link to Gutenberg) is distinctly cat-like.