The difference being Amiibo are almost always frivolous add ons versus being really needed content, people who obsess about having every little thing are the only ones who will have an issue here, and they need help in other ways.
I think the whole Battlefront II pay-to-win fiasco is really changing the narrative of what's considered legitimate DLC. DLC has always had items with a hefty level of frivolity to them. DLC that is purely cosmetic does not get a free pass as somehow not being DLC simply because it does not change the mechanics of play. One need only to look at the number of fighting game skins to recognize that frivolous DLC is not only a perfectly valid form of digital content but is also incredibly popular.
Lately, it seems like Overwatch is getting a magical free pass on its exploitative gambling-esque loot box system simply because gameplay is not altered with the prizes. Those skins are DLC. Highly coveted, and yet totally frivolous, DLC.
Amiibos offer mostly frivolous digital add-ons, but they offer them in an exclusive fashion that make them a very difficult kind of DLC to forgive due to the known trouble that Nintendo has with certain Amiibo stock.
So, yeah. Amiibos are DLC. They often times offer content that can not be earned in the actual game. And even frivolous DLC should not be locked behind a product that is difficult for many to acquire due to stocking issues.
Extra Addition (via Edit)
I think many of us are also disregarding that experiences of play, even when mechanics remain unchanged, can be altered with purely cosmetic changes because of the way those cosmetic changes affect our personal experience of a game's scenario. For example, Fat Drake. Yes, I know he's not DLC. But playing uncharted with Fat Drake, though it does not change any mechanics, it can completely change the experience. A lot of frivolous DLC is like that. Without affecting game mechanics, they manage to affect our enjoyment. It's totally a thing.