Because the non-magical one is tapping into the source in a different fashion? Druid: "I'm bendin' nature man! I'm usin' nature magic man!" Barbarian "I am tapping into my inner beast, man. I'm one with the primal force of myself."If the barbarian is nonmagical, then the druid also has to be nonmagical; how can a power source be magical in nature for one class, but not for another?
If you mean no supernaturalness, then only martial classes will likely fit your tastes, and there are no rumors of any more.
Part of the problem is the overlap between supernatural warriors and purely martial warriors. Take a lightly armored, asian-themed "wandering swordsman" archetype- it could be made as a purely martial character, or it could be made with ki powers. Probably the best way to run things would be to declare it a ki character class, then make two builds- one that's heavy on the supernatural ki elements, and one that uses the more physical ones.... and not much room for others that would apply in most D&D settings, either. I mean, you could sort-of squeeze in a Swashbuckler as a lightly-armored martial defender. And maybe a non-mystical martial artist and a mounted warrior type.
You can even argue that no class in 4E is nonmagical as the only really satisfactory explanation of encounter/daily exploits which doesn't falls apart is that they are also magic powered.