Can Mordekaiser, Dominating target Baron Nashor

No — Mordekaiser, Dominating can't choose Baron Nashor.

Mordekaiser's trigger says "you may discard 1 to kill a unit or gear." Because you have to select a specific permanent, that choice is targeting (Rule 355.10.d: "Kill a unit. Its controller draws 2" targets the unit), and Baron's "I can't be chosen by enemy spells and abilities" makes him untargetable to it (Rule 757). Same reasoning as the existing ruling that The List's activated ability can't pick him — an activated or triggered ability is still an "ability" for this protection.

The trigger still goes on the chain and resolves normally, and you can discard to kill some other unit or a gear instead — or simply decline to use it. Bonus note: his "As you play me" replacement still puts him in the Baron Pit, which is unrelated to the kill ability.