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

Could you please rephrase this in a more natural way?

in Russian:
If online in version 3.0, certain features that modify the standard SoD rules are enabled (e.g., bug fixes or starting the timer after a turn is taken), then they are enabled for all players, and they compete on equal terms.
However, if an offline tournament is held, and one player plays with a pure SoD version, while another plays with version 3.0 with modified rules, their results cannot be compared within the same tournament. However, their save files are identical, and as a result, it is unclear according to which rules the game was played. This is incorrect.

In RC5, a replayable quick start without magic was added unilaterally (i.e., it was possible to play with this feature against a version without this feature online), while in the original SoD, 1. it is impossible to conduct a quick start without magic under any circumstances. 2. online, it is impossible to replay a quick start.
This is unfair, so in RC6, the replayable quick start without magic was linked to the ImprovedGameplay option (what this means, see the description of 3.0).
Furthermore, this decision will be changed to benefit everyone and ensure fairness