It's intentionally reductionist for a reason. Mythic is magic with an artificial distinction. Much like how people argue till they are blue in the face that psionics is not and never should be classified as magic, even though psionics is a clearly supernatural. To me this feels like the kind of hair-splitting of "don't call my psionics 'magic".
Batman is supposedly a peak human with no supernatural abilities. Same thing with Black Widow, iirc. Or Green Arrow. Even in a world of Gods and Monsters, they don't do anything more than a "peak human" can do. This is where I would put the limit of the "nonmagical fighter". They can do what a peak human can. If we're not making the fighter have supernatural abilities, this is my limit.
If we are going to give them supernatural or mythic abilities, you gotta name a source. Wolverine is a mutant, Hulk was blasted with gamma radiation, Cap was infused with super-serum. If you're transcending what a normal mortal can do you gotta say how.
Dragons are innately "magical" creatures. They can do things fantastical because they are born fantastical. Now, if you want fighters to do fantastical things, they must either be born fantastical or somehow become fantastical. In D&D, neither is particularly hard to do. But you gotta explain why suddenly your swordsman faster than a speeding bullete, more powerful than a lightning rail and able to leap tall towers in a single bound. Give me something.
I'm not asking for a fighter to cast spells, nor do I want him to reign in mediocrity. I just want a little more justification for why he can now do superhero mythic bullocks other than "he's 11th level now."