While it's likely forbidden as bal teshaktzu (as noted by @mbloch) and as tzaar balei chayim (causing animal suffering), swallowing an animal whole would seem to be no more derekh hanaathan (in the way they are enjoyed) or k'derech achila (in the manner of eating) than is swallowing a pill, which is also not considered halachik eating (at least on a bibilical level). See e.g. Shulchan Aruch YD 155:3:
בִּשְׁאָר אִסוּרִים מִתְרַפְּאִים בִּמְקוֹם סַכָּנָה, אֲפִלּוּ דֶּרֶךְ הֲנָאָתָן. וְשֶׁלֹּא בִּמְקוֹם סַכָּנָה, כְּדֶרֶךְ הֲנָאָתָן אָסוּר; שֶׁלֹּא כְּדֶרֶךְ הֲנָאָתָן, מֻתָּר, חוּץ מִכִּלְאֵי הַכֶּרֶם וּבָשָׂר בְּחָלָב שֶׁאֲסוּרִים אֲפִלּוּ שֶׁלֹּא כְּדֶרֶךְ הֲנָאָתָן אֶלָּא בִּמְקוֹם סַכָּנָה.
With other forbidden (therapeutic food item) one can be healed when mortally (ill) even in the manner they are enjoyed (i.e. normal consumption). And when there is no risk (of dying from the illness), it is forbidden (to partake of the forbidden therapeutic food item) in the way they are enjoyed, but it is permitted (to consume them in a manner that is) not the way that they are enjoyed, except for kilei hakerem (produce of forbidden vineyard mixing) and meat (cooked) in milk which are forbidden even not as they are enjoyed, except when in mortal danger.
This halacha is referenced by kashruth agencies (such as the Star-K) when allowing the swallowing of nonkosher medication:
Those listed above may take non-kosher medication shelo k’derech achila, in an uncommon way of eating, if a kosher alternative is not readily available. Items which are designed to be swallowed without chewing (caplets, swallow tablets, and even gelatin capsules), poor tasting chewable tablets, and poor tasting liquids have a shelo k’derech achila status. For example, if someone has the flu, and the only fever reducer available is a non-kosher gelatin capsule, one may swallow the product. Similarly, one may swallow Celebrex in a gelatin capsule or tablets containing chondroiton (derived from non-kosher bovine trachea cartilage) for chronic debilitating arthritis pain. However, under normal circumstances one may not take non-kosher products if it requires eating in a normal manner (e.g. non-kosher chewable tablets that taste good).
Considering that, as opposed to pleasant tasting, chewed food items, the surface of the skin of a live frog is unlikely to trigger a pleasurable gustative sensory response in the throat, it would seem swallowing even a dead frog whole, should not be considered halachik "eating".
See also here.