Are enemy Dragon's Shouts tied to magicka?
Solution 1:
Ok, so, Skizzlefrits reminded me of the wonders of the console. So, I popped in for a while and decided to try it out.
Long story short, the dragons were not too pleased that I likened their mighty thu'ums to mere magic, and proceeded to shout at me for quite a while.
The Riften guards weren't all that thrilled with me either. Something about how crazy experiments belong in Winterhold...
Result: If the dragon's shouts are tied to something, I don't think it's magicka anymore.