Is it some form of ancient magic, or is it something else?
Yes, it's an ancient form of Nord magic taught to the Nords by Paarthurnax and Kynareth. Dragons are magical creatures. Even their ability to http://www.uesp.net/wiki/Lore:King_Edward,_Part_XII is magical. What sources have you seen that say the thu'um is not a form of magic?
You might want to take a look at these UESP lore pages which describe the magical nature of the thu'um without too many spoilers.
http://www.uesp.net/wiki/Lore:Thu%27um
http://www.uesp.net/wiki/Lore:Magic