1st offline tournament

Dear users, I have a small question...
So, does this mean that a necromancer hero
cannot use their skill?
If demonology is not necromancy, then what
is it?
I remember that there was no such skill in the third game.

The skill can be used, but the summoned skeletons cannot be taken to the arena; you can find another use for them. But this is also a limitation for this round! See Horna's post regarding demonology. All these restrictions are to prevent the entire game from being reduced to just chasing skeletons and demons.