HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

It seems unfair to me that the ability to determine the turn order, remember it during battle, and account for all influencing factors is an unnecessary part of the game that should be eliminated!

Out of everything described above, this sentence only affects the second point.

Added 9 minutes later
By the way, a question for Dirty. Why do they record chess moves? Doesn't it affect the gameplay?! Someone might forget something and mess up, and you can win because of that...

It's the same here. It's just a battle, like a mini-game of chess. Nothing лишнего...