Magic Damage is a type of Elemental Damage in Diablo I and Diablo II. In Diablo III, it was replaced with Arcane and Holy damage.
Diablo (Game) examples include:
Zombie (Diablo I) were also immune to magic in the Normal and Hell difficulties, but not Nightmare.
Diablo II examples include projectiles shot by the Abyss Knights and Oblivion Knights with a purple glow on their hands. They did not have an official name back then.
So, the damage type can only be officially be said to have named in Diablo III.
Magic damage was also represented by the color white in many class skills.