(If I’m a bit cranky, it just because I don’t have time to be nice )
I’ve seen this argument before and its a tad annoying because it only applies to dragons. If I called an elf a dwarf, and an orc and elf. Readers would just be confused and annoyed, they wouldn’t defend my right to call my fantasy characters whatever I liked. If I advertised a book about mermaids, but my mermaids were bird people, readers looking forward to mermaids would not defend my right to attach mermaid to whatever I felt like, simply because it doesn’t exist. A dream doesn’t exist, you can’t prove it’s existence, but I’m not just allowed to use the word however I like because I can’t take a picture of it.
Since the only thing I can find out about you is D&D, I’ll use that in my example.
And yet D&D provides an illustration and a list of characteristics for most monsters. They don’t just say, it fantasy, it doesn’t matter what it looks like or what it does, I can be and do anything you want. If my DM said I was being attacked by a dragon only to discover it didn’t resemble or act like a dragon in any fashion, they might as well have said I was attacked by a thing because the word “dragon” has lost all meaning.
I believe D&D has broad term that applies to everything dragon, I want to say dragonkin, but that might be Warcraft, but only dragons are actually dragons. And like snakes, D&D has different kinds of dragons, but that doesn’t make an alligator or a gargoyle a dragon just because they have a lot in common. Even an undead dragon isn’t technically a dragon anymore.
I feel like this is a contradiction, or perhaps a mild example of cultural corruption or appropriation. To say “all these cultures have creatures that are different from each other, so how can you define them” then basically add “But I wish they were all called the same thing and stopped being their own creature.”
The fact that Eastern and Western dragons are so different is probably reason enough they shouldn’t be related. We call them dragons because we’re lazy and it means we only have to learn one word, because its an English-ish word rather than a Chinese word, and because it would be impossible to get people to stop calling them dragons at this point, not because it’s “correct”. We don’t call all these creatures dragons because they are all basically the same. We call them dragons because coming up with and remembering the names for all these equally weird creatures would be hard.
This is all my opinion, of course.