Dragons are innately magical, yes. That doesn’t mean their flight is an act of magic. It’s simply a facet of their nature. And I notice no one wants to address giants existing and being able to stand, and walk, and not collapse under their own body weight.
The current fighter is not even supernatural. But it could be, and their supernatural abilities would not need to be defined as magic. Again, if giants exist, why can’t Goku?
Dragons are magic in every sense. I was reviewing the 2014 Monster Manual.
I read this to mean the Dragon breath is explicitly magic. "Dragons are also
magical creatures whose innate power fuels their dreaded breath weapons and other preternatural abilities." It can also be understood to mean that its preternatural method of flight is likewise explicitly "magical", because the magical creature does it in a magical way.
Meanwhile, in a Variant textbox: "Dragons are innately
magical creatures that can master a few spells as they age, using this variant." Here the magic of a Dragon can extend to casting spells innately, but typically includes nonspell magical traits.
The Lair Actions including features like "
magical darkness" and "
magic fog".
"The region containing a legendary ... dragon's lair is warped by the
dragon's magic." "A legendary white dragon's innate
magic deepens the cold in the area around its lair." And so on.
All of these "preternatural" traits are explicitly "magic" according to the rules of D&D 5e.
It seems unsustainable to posit such high tier features except by the means of magic.