The author of the article you mentioned (Alex Howe) is a good example for what I insinuated: He takes issue with Korsgaard's argument (and, it seems, Kantian ethics more generally), but in his PhD thesis argues for granting "basic citizenship rights" to domestic animals (including farm animals), which is arguably a far more radical position than veganism, which merely posits that it is immoral to exploit (or be cruel towards) animals (e.g. as a food resource). Either way, if you have an issue with Kantian ethics and how they are applied to animal rights, I suggest you take it up with a Kantian (which I am not). And, even if I am repeating myself, none of this has any direct relevance to my earlier point, which is that many moral philosophers from many different schools of thought (including, but by no means limited to, Kantian ethics) have arrived at conclusions which are at least similar to the basic vegan stance, i.e. that unnecessarily causing harm to (sentient) animals, e.g. by exploiting them as food, is immoral.