[Rolando]

I think perception of danger is what is important. If the salamander feel threatened by the non magically armed fighter it will be engaged.

With the same idea in mind a big, powerful, magical creature may feel non threatened by a fighter and ignore it, in practice not being engaged by the fighter but maybe allowing the fighter an attack as if attacking the target from behind (?).

If there is no GM and this is a competitive and tactical scenario or board game type game I would say the salamander is engaged even if it can't be harmed, because the rules are clear there, even if they make no sense, that is what a GM is for, in part to adjust rules to make sense in cases like this.