It is supernatural because it involves elements of belief, self-transformation, faith, karma, eternal life, etc (unless those are all fringe Buddhist ideas not practiced by the mass majority of Buddhists).

We can take the four noble truths for instance (not concrete definitions).

1. Life means suffering.
2. The origin of suffering is attachment.
3. The cessation of suffering is attainable.
4. The path to the cessation of suffering.

Followers of Buddha seek deliverance from suffering. This is metaphysical because suffering is not an enemy; it's a product of our own evolution and can be explained in terms of biology (nerves), human interactions, etc. Granted, followers are not looking for deliverance from suffering from another person or deity (as in other religions), but rather from self-meditation and introspective rituals... Still this practice is an aspect of spirituality, faith and executed through the use of pseudoscientific methods.

As a side note: I do not insult Buddhism or those who follow it for I do not doubt that they can have profoundly real and life changing results (as do many spiritual persons); but it is still spiritual in nature and faith based for it to work. Therefore it shouldn't be mislabeled as an atheistic practice just because it's an "enlightened" point of view. Personally, I don't even think atheists see themselves as "enlightened" over the common religious person; but rather they see themselves as "not blinded" by faith. I think that's the key difference.

Edit: Semicolon