This is a pretty common activity found in hunter-gatherer economies, irrespective of culture.

When a kill is brought home the extended family gathers around to process the meat for storage.

The rare and/or uber-nutritious parts of the animal are usually eaten immediately. These articular parts of the animal, and who gets to eat them, usually carries social and symbolic significance.

While this alone might put their eating on the floor in context, there's also the fact those western kitchen counters probably aren't designed to support a + 200lbs, freshly killed seal.

Anthony Bourdain has always seemed like a pretty unapologetic carnivore; I wonder if the producers didn't make him include those couple minutes of cringing because of aw seals, etc.

I love Anthony Bourdain, and I guarantee you he doesn't care about the seal. Still, it's pretty unrealistic not to address the strangeness of eating raw flesh from a bloody carcass on the kitchen floor. Without Bourdain's apology, we may as well assume that was formerly a particularly difficult Inuit child.