See, and IMO, this is an example of 4e being inconsistent. Certain powers it clearly marks as "magical" through keywords... but others it leaves unlabeled. As a DM, since it doesn't have the Arcane keyword I would be tempted to rule that neither of these abilities is magical especially as they pertain to the Arcana skill and using it to modify, detect, etc. these powers... of course then we have feystep which, IMO, seems clearly magical yet has no arcane keyword either... I think rules wise there is a strong argument for the need to draw the distinction.
Not all magic is arcane. unless you don't call divine magic or primal/druid magic magic.
Another thing here - let's say Fighter cannot possibly do something fantastic because fantastic automatically assumes they use magic, and that violates the idea of them being just "martial dudes", so to speak.
Why even have a level 20 Fighter? What does Level 20 even mean if a Level 20 Wizard is superpowerful but a Level 20 Fighter is weak?
3E basically said there are wealth by level guidelines so that a high level Fighter has the necessary equipment to deal with equal level threats that may have magic at their disposal.
Alternative, maybe Fighter Levels just stop at 10, and afterwards, you become "Supernatural Warrior", maybe sacrifie your soul to some demon or swear and oath with a god or learn sword magic or acquire a fantastical magic artifact, but you get magic abilities that bring you en par with equal level "traditional" spellcasters.*
But what I just cannot see ever leading to satisfying play for me is the idea that a high level fighter is mundane and outshined by spellcasters. Either there is no high level fighter without magic abilities, or we define that in a fantastic world of Giants and Dragons, you don't need magic spells to do so fantastic things (it just helps.).
Of course, you could say levels are just a number to indicate when you get new abilities, it doesn't tell you if the abilities are good or as powerful as abilities from other classes. But then you're removing the game even further from anything I want to play. Not that you can't do that, I am just saying. t's hardly as if you need me on this ride.
*) That's kinda 4E imlicitely did - it introduced Paragon Pathes and Epic Destinies to highlight: "You're not just a Fighter Dude anymore." Whether people actually played this transition as meaningful is another matter.