If you are going to quote from the PHB, you could at least quote all the relevant bits.
At Will Powers They represent easy weapon swings or simple magical effects that don't put any unusual strain on you or tax your resources in any other way.
Encounter Powers Encounter powers produce more powerful, more dramatic effects than at-will powers. If you are a martial character, they are exploits you've practiced extensively but can pull off only once in a while.
Daily Powers Daily powers are the most powerful effects you can produce, and using one takes a significant toll on your your physical and mental resources. If you're a martial character, you're reaching into your deepest reserves of energy to pull off an amazing exploit.
Both encounter and daily powers use the phrase "Pull Off" for martial characters.
Google definition for "Pull Off"
be successful; achieve a goal; "She succeeded in persuading us all"; "I managed to carry the box upstairs"; "She pulled it off, even though we never thought her capable of it"; "The pianist negociated the difficult runs"
This comes closer to implying a narrative control sort of explanation than it does anything else.
Uhm... this would be great evidence... if arcane spells, divine prayers, etc. didn't all work the same way. You can only pull off an encounter divine prayer... once per encounter. So how does this in anyway support the fact that they are not magical and based around narrative control...Nowhere in the descriptions do I see a reason why you can only pull off an exploit once per encounter or day. Again not seeing how this supports narrative control as opposed to non-traditional magic... what it is, is blatantly vague about reasons and thus we refer back to the definition of martial power...
unless you're arguing every spell, prayer, etc. is not magic (though the book states they are in the traditional sense) and instead are bits of narrative control since they all work, mechanically, on the same structure.
Or are you arguing a power can be both magical and narrative control... which then does nothing to offset the argument of some martial exploits as non-traditional magic. And while martial encounter powers are vague as toi the reasons one cna pull it off only once per an encounter...martial dailies do talk about drawing on energy as a reason they can only be performed a limited number of times...which along with the definition of martial power supports a mystical or magical definition.
Also,
This phrase "Martial Powers are not magic in the traditional sense" is immediately followed by " although some martial powers stand well beyond the capabilities of ordinary mortals"
The reason for the first half of the sentance is given in the 2nd. Martial Characters are not necessarily realistic or bound to what people in the real world can do. This is a far cry from saying they are "Magic"
For further explanation, see T.V. Tropes
Charles Atlas Superpower - Television Tropes & Idioms
Badass Normal - Television Tropes & Idioms
First, I don't understand your first two paragraphs... are you really argument they have t say it's "non-traditional" magic as opposed to "not magic period" because it allows things that are beyond the realm of normal people... but it is not in any way magical?? Is that really what you're arguing? Because if so, I ask again... why not just say it is not magic period, but allows the player of a fighter to gain narrative control for a few moments?? I'm not buying it.
Also, if you're going to use this argument... you've got to stick with the established (up to the point of 4e) tropes of D&D (not those of superheroes which is arguably a different genre with different tropes) in order to have a baseline? I mean tropes are based on a specific genre and since D&D is it's own genre the only way to claim an action is a valid trope of it is to examine it's tropes up until the element under scrutiny was introduced. That's why this really is a bad argument to try and use... in fact IMO, worse than narrative control, but anyway...
So tell me what edition of D&D allowed fighters to force numerous opponents to move adjacent to them and allow him to attack them with no chance to resist?... what edition did they get the ability to regenerate in? What edition was it that a Rogue was able to become invisible without the aid of magic? basically I'm asking when were these supposed tropes of D&D introduced over it's 30yrs+ lifespan.
I guess more importantly for you to push this argument, what I'm asking is what is the basis for the tropes of D&D and what criteria are you using to determine them... since as far as I know there is no official tropes of D&D list? Again why this is, IMO, a weak argument to try and prove or disprove.