There appears to be no default, and therefore we're stuck.
I've found the following quote on page 171 of the PHB, emphasis mine
In the event that a class feature, domain granted power, or other
special ability provides an adjustment to your caster level
and I have also found the following in the PHB's glossary, emphasis mine again
granted power: The special ability a cleric gain from each of his
What does this tell us? As the DMG rules that there are only three types of special abilities: Extraordinary, Spell-like, and Supernatural, we know that granted powers must be one of these three. However, if we look at the Spell Compendium, we find several granted powers that are explicitly marked as either Ex, Su, or Sp, and many more that are not marked at all. This forces us to conclude that there is no default answer. If there was, they would not have found the need to use all three labels and leave some unlabelled.
So what can we do now that we know that there is no default? Personally, I think we're stuck. We have several granted powers that are not labeled as being anything, but must be either Ex, Su, or Sp, but I know of no rules text that tells us what to do in this case. In fact, I know of none that acknowledge this problem and I found nothing in the PHB, DMG, Complete Divine, or Spell Compendium that helps. Because we cannot say what type of ability these unmarked powers are, we cannot rule on if they are inherently magical or not.
That being said, some of the untyped domains in Complete Divine, namely Dream and Madness, give us fluff reasons for the granted power:
(Dream Domain) Because you have long delved into dreams and nightmares, you are immune to fear effects.
(Madness Domain) Your insanity gives you insight. You subtract 1 from all Wisdom-based skill checks...
which may give us reasons to suspect that the default is Ex, but this is clearly not a good hill to stand on. A safer hill would be to treat them like you would a class feature that isn't marked as Ex, Su, or Sp, but that would contradict the PHB's claim that they're special abilities and the DMG's claim that special abilities can only be one of those three types.
On the bright side, we don't need any special rules for the abilities that are marked as being something.
Or maybe they're natural?
Hey I Can Chan's comment helpfully points out a contradiction between the PHB and the DMG. I can't remember this fact being acknowledged by any of the domains, but page 180 of the PHB clearly lists natural abilities as being special abilities and says
Natural abilities are those not otherwise designated as extraordinary,
supernatural, or spell-like.
If you take the PHB's approach over the DMG's, then the answer follows easily from here. If a granted power is marked as being something, then it's that. Otherwise, absurdly, the god-given power is natural. If you instead agree with the DMG, then we're back to not knowing what to do (as above).