I use my "fantasy common sense" when it comes to this question. Most "supernatural" things I consider magic, however, I do not go expressly to the "if it breaks the laws of our Earth physics, it is magical" ruling though. This is because (as
@MatthewJHanson mentions) it would mean creature sizes and the ability to fly at those sizes would make these creatures and animals have to be magical. And that's... I just don't feel the need to go that far. It doesn't break my "fantasy common sense" to think a Giant Ape could exist, or that a pegasus could fly with its wings able to lift its body, or that a fighter could actually cut through dragon scale (and maybe even kill a dragon) with just a regular sword. Yes, those all break our Earth-physics... but I'm willing to accept "fantasy world physics" could allow all those to happen without requiring to be "magical".
But anything related to the castings or use of spells or enchantments (including arcane, divine, primal, psionic, runic, alchemical etc. etc.) I say is Magic. Because that stuff is exactly what my fantasy common sense tells me should be Magic. Being able to read someone else's mind is Magic. Having a sword that can spontaneously burst into flame is Magic. Punching someone and having their entire muscular system fail and shut down is Magic. Being able to innately turn invisible is Magic. And so on.
And in terms of
Dispel Magic or an
Antimagic Field... those are both so inconsequential to any D&D campaign I have played in or run that I never, EVER worry about trying to make a cohesive rules system about it. Hell... I think the
Antimagic Field is the least-used trope in D&D that somehow gets thrown around the MOST for arguing why something or some rule in the game should or shouldn't exist. With the amount of times
Antimagic Field gets used as a talking point, you'd think it'd show up in every campaign like every-other session. But they like never or barely-ever actually get used, because it's a rather lame trope in the first place. Maybe one time in a campaign a DM might throw it out there for a unique surprise... but that's pretty much it. It's never been worth the words spewed on its behalf talking about stuff in the game in my opinion. And thus I never even think about it.