It is not a euphemism at all. It is merely a matter of a spelling change based on a change in pronunciation (as arse is pretty much unknown in the US.) It is likely that the New England accent figures in here; in certain neighborhoods in Boston, for example, arse and ass would be pronounced identically, and there would be no audible "r" in the word at all. One might consider the Boston-accent joke "Q-what are khakis? A- What you use to unlock and start your car" to get an idea of the accent being described.NB Note that Americans use the word ass for the British arse, to mean buttocks or anus. This may have started off as a euphemism in America,
Since the Spanish has been mentioned, it's worth noting that the distinction exists in other languages too. A "burro" is a domesticated "asno".And if you are writing in English about this pack animal in South America, it is usual to use the Spanish word "burro".
Recently I got acquainted with the work of art called "The Nativity of Christ". It is on display in the Hermitage museum in Saint-Petersburg where I am working as a tourist guide. This artwork is made of majolica, which is burnt clay covered with glaze. The plot behind this relief is well-known. Infant Christ is lying in the manger, the Virgin is sitting next to him observing her child, St. Joseph looks sad and is sitting aside and the shepherds are adoring Infant Christ with one of them following the guiding star. Another very important detail is an ox and an ass standing beside the manger. When I first saw this description in English (written in other words, of course), I wondered why "donkey" was wrong in this context. Now, I think, I have found the reply to my question: because "ass" is always used in biblical contexts.Normally ass and donkey are the same animal, but ass is used more often, though not exclusively, in a metaphorical sense (Don't be such a silly ass!), and in an archaic or bilbical context: Thou shalt not covet thy neighbour's ox nor his ass etc. Also, it was either Nero's wife or Cleopatra or both who bathed in asses' milk (nobody says donkey's milk here). The wild variety of the animal is always referred to as an ass not a donkey, so that must be why both ass and donkey appear in your list.
It comes to my mind that the domesticated donkey is a specific species (actually, subspecies, even) Equus africanus asinus.It seems to me that donkey is specifically the domesticated animal, whereas ass covers both domestic and wild forms. So, strictly speaking, it was not necessary to include donkey in the list.