>e.g. from oil of Schizochytrium, a non-plant non-animal unicellular living being, which is falsely named as "algae" by vendors, to sound more like a vegetable to vegan ears
You seem to be implying here that Schizochytrium is not a vegan product, even though "non-animal" is completely sufficient to meet that criterion.
I agree that, as you say, being non-animal is sufficient.
Nevertheless, I find it funny that the vendors have felt the need to use the word "algae" for marketing this product.
It is true however that while "algae" is incorrect, there is no appropriate word to name them that would be easily understood by the general public.
At most they might be called "protists", as in many biology manuals, which is a word that I strongly dislike as meaningless.
("Protists" means "the first", but among which and according to what ordering criterion? "Protist" is a word normally used with the meaning "unicellular eukaryote" a.k.a. "unicellular nucleate", but one should better use the words that are meant.)
You seem to be implying here that Schizochytrium is not a vegan product, even though "non-animal" is completely sufficient to meet that criterion.