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

the difference is that it will say griffins fly here, griffins fly here, griffins fly here, griffins fly here... but it's unclear which ones and where, and you can't reconstruct it from the battle log.

You still haven't answered what the difference is between recording moves in chess and here. Why is it necessary there, but in Heroes it affects the gameplay?

Moreover, we're not even talking about the moves themselves, but simply about numbering the units.

And even with numbering, it will still be unclear which griffins are flying where...