That's according to the OED. I think others are reacting to the (false) notion that dignity can only be reserved for humans.
I wonder if the distinction in how people think about dignity could be correlated with pet ownership? I’ve never had a significant pet (gerbils, and now ferrets), and I would never project that definition of “dignity” on an animal.
But I know horse owners who would use many of those adjectives to describe their horses (and interestingly, most would never use the word “pet”). I like horses; I don’t think I’d ever purposely eat horse meat. But to me they are still just animals.
And frankly, I don’t know how horses really think. So I don’t know what treatment they would consider noble, even if I cared. But if I did care, I would doubt that being stuck in a stall, only to be brought out to have stuff strapped to my back so someone can climb on me and make me dance to their bidding, would be noble.
But how would I know — maybe they are like the Ood, existing only to serve others. (random Dr. Who reference).
I don’t think any human would find what we do with horses to be dignified, noble, or treating them as worthy or honourable. But on the other hand, they are animals, so why would be apply those same rules.
Which is my way of showing why I don’t think of them as any more than animals, and don’t bother with “dignity”. It’s an unknowable thing — how to treat something we can’t communicate with in the way they would find “dignified”. If I care, I get stuck in a circular argument that ends with me freeing the horses and letting the run wild — not because that is dignified either, but because then we are at least “leaving them to their own devices”.