@pavel94
Finite lifespans? No, I don't think that was ever stated that Youkai, Lunarians, Ghosts, Fairies or Gods had those, maybe there are a few outliers. Should things keep going smoothly they will live indefinitely.
As for why the Houri are singled out in canon it all depends on how you choose to define immortality. Never aging is considered biological immortality, Magicians have that. Fairies have Resurrection Immortality in that they re-animate after death so long as there is nature. Some Youkai have regenerative immortality so long as you don't have their one weakness like a stake through the heart for vampires they'll self repair. Akyuu does it through a reincarnation cycle(as do most others but they don't remember it). Gods keep existing so long as there is faith and many Youkai are often the same when it comes to fear.
Where Touhou chooses to make the distinction is that for the above entities, given infinite time something will likely kill them eventually like being forgotten, being sealed away forever, having their weakness exploited, the sun going supernova ect. Houri on the other hand have complete immortality, they live no matter what happens to them period. This is achieved not through regeneration or rebirth but through Kaguya's time manipulation, simply put what is done to them is undone.
So Houri are the only canon immortals in Touhou because ZUN uses the strictest definition of Immortal. I was using the more expanded definitions, like the type you see in scientific articles about stopping aging.