Dude these are the same thing
No they're not. Denying that something is traditional magic is not the same as asserting that it is non-traditional magic. Nor does it entail that it is non-traditional magic. At most it raises a question - "OK, is it non-traditional magic, or is it something else altogether?" The paragraph in question goes on to explain what it is - it is the ability to do extraordinary things that ordinary people can't do, and it is not like clerical prayer or casting a spell. Whether or not it is a type of non-traditional magic - whatever exactly that might mean - is left open.
4e is the first edition to explicitly label a fighter's abilities as such... or is it not magic?? Which one are you now claiming it is?
It does not explicitly label fighter's ability as magic. It explicitly labels them as being something other than traditional magic. That could include either non-traditional magic, or non-magic. (Should I draw a Venn diagram?)
As to which of those it is, I've now repeated over several posts that the game leaves it open. I even quoted an epic destiny description where you can see the game authors leaving it open - an Eternal Defender might be infused with divine power, or be driven by implacable will. That's a deliberate design decision, the purpose of which is to make it viable to write up sufficiently epic powers for martial PCs while leaving it open for any given table and any given player how they want to handle Hercules, Aragorn or Beowulf at their table.
The key thing is that martial powers don't have damage keywords such as acid, cold, fire, lightning, thunder, force, psychic, radiant or necrotic. That is, they're nearly all untyped, ordinary physical damage. Some deliver poison damage, but if you look at those powers (eg the Executioner Assassin) it's clear that those actually involve brewing and applying poisons.
Martial powers don't have teleportation keywords (except for the rogue spell-thief power that let's you piggyback on someone else's teleport). They don't have zone or conjuration keywords (which are the actual targets of Dispel Magic in the 4e system). And they don't have the illusion, charm or sleep keywords (so, for example, the rogue abilities that permit invisibility don't have the illusion keyword - they are not illusion spells like the wizard's Invisibility spell, which does have that keyword - the invisibility is simply a mechanical implementation of stealth without the need for a roll). In other words, martial abilities do not generate magical effects. They generate the same sorts of effects that fighters and rogues have always produced in D&D - weapon attacks, jumping, hiding, dodging blows, etc.
No one denies that the mechanical implementation is different from other versions of D&D - in particular, there is a much more rationing-by-limitation (eg a rogue being able to turn invisible once per day) than rationing-by-lottery (eg a rogue making a Stealth check to hide), but that is about mechanics, not about the fiction. If you project expectations from 3E or PF about mechanics-to-fiction correlation, as [MENTION=17106]Ahnehnois[/MENTION] does, and hence assert that because a rogue's power is rationed by usage limitations it must be a spell, you are simply missing the point of the mechanics, which are precisely intended to decouple player choices from character choices in certain cases, and to replace ration-by-lottery with other forms of rationing. 4e is hardly the only RPG on the market to do this, even for non-magical abilities.
Well seeing as the troll's ability is a racial trait, that every single one of their race has I'd argue there's an argument for it being biological??
What does that even mean? It's a racial trait of a pixie to turn invisible, or of a dragon to breathe fire, so they're biological too? When you're talking about a fantasy world, with being who can breathe fire and turn invisible and regenerate decapitated heads as part of their inherent nature, there is no obvious contrast between biology and magic.