*Cracks fingers and positions keyboard* Let's get started then.
His Japanese name, Symboler, may be a combination of symbol and bora, a wind traveling the atlantic, and the Sun god Ra. But put aside speculation, Sigilyph is by definite a mixture of sigil and glyph. It may also draw its name from "sylph", which was a spirit of the air according to folklore.
Okay, now let's go to what it's based off of.
Sigilyph shows most comparison to Kachina Dolls, which by information from Heard Museum Shops, is "are representations of the Katsina spirits. The carved figures are given as ceremonial gifts to young girls by the Katsinam. Each gift represents a prayer wish for good health, growth and fertility."
It may also be from the Nazca lines, specifically the fourth one on a google search, but not much information on that one. It was Bulbapedia so I have some credibility there. Oh, did I mention Nazca lines are also found in the desert?
His french name, Cryptéro, means Cryptogram and Pterodactyl.
So if this featherless "bird" was a bird, I would see a bit more evidence to support it. Because by the looks of it, because if this wind chime is a bird, it's one pretty routed out bird.
Here's my only qualm with this. Sigiliph in the dex, given to it by GF, is classified as the Avianoid Pokemon. REGARDLESS of what it is based off, GF specifically meant for it to be classified as a bird like creature. They could have easily classified it the same way as Golurk, with the "Automaton" classification, but it is specifically supposed to relate to birds.
By this same classification method, we could debunk Dodrio as a bird, as all birds have wings, yet Dodrio doesn't (sure it has bird like qualities, but because it lacks wings it isn't a bird). Based on what you've said, Sigiliph should not be considered the
Avianoid Pokemon, but rather, the Sigil or Pterodactyl Pokemon, based on its name alone. But it isn't and is SPECIFCALLY placed in a category relating its closest species to being that of a bird. I'm not saying the information you provided isn't true, but GF specifically chose its classification to relate to birds at the least, with no mention of it having anything to do with Sigils, Reptiles or Kachina Dolls.
Lastly, phrases and words like "shows most comparison to" and "may also be from" literally show that that is a speculation, not a fact. Avianoid literally means Bird Like, as Humanoid mean Human Like. In this case, since a direct species classification is not given for it, you can only say it is "of or relating to birds" as there is no mention of it solely having autonomous intellect, as well as there no mention of it being composed of inorganic parts.
So again, unless you can show me clear, concise, factual evidence in the game or stated by GF otherwise, or even outside the game that specifically details Sigiliphs' anatomy, not "what ifs" "maybes" and "most comparisons", it's most closely related to birds, which in this case, is a fact backed up by the game itself, and makes it if nothing else, a bird like creature.
Edit:
Fascinating. I'm even more intrigued by Sigilyph now. I read up on serebii, as it states, "Known in ancient China as the Xiàngzhengniao", a mythical being of sorts. It is said in the dex it's an Avianoid pokemon, so idk what to make of that.
Precisely the only reason I'd consider this a bird is because of that: Avianoid meaning bird like, and no other description ever being given about it otherwise that states it is otherwise.