I find that there is Magic in AiME, but not "Spells" in the D&D sense. Magic abilities come through Feats (Virtues in the game) and are more linked to Culture (Race) than Class. For example, Dwarves can know spells of opening and shutting, Wood-Elves can light and extinguish lights, and induce magical sleep. Dunedain can feel the presence of wraiths, wights, shades and the like even if they are invisible to other members of the party.
But it is far more limited that D&D that's for sure, stuff that would be cantrips in 5e mostly.
So if players consider "Magic" to be Fireballs and Magic Missiles then, oh yeah, this is going to feel like "No magic" for sure.
I'm not sure how TOR would be any better in that regard except to say you don't have the same expectation of what "Magic" using a different ruleset for the same adventures.