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

Nope, I tried both through the launcher and via the created exe directly, something else is broken...

Judging by the screenshot, this time you have hvrules 1.40 connected, but the other side does not. That is the problem.
But yes, the message is not informative. It especially confuses newcomers — they start worrying about what version 3.2 and 4.0 are.
(3.2 - SoD, 4.0 - Complete; they are fully compatible and connect if the same hvrules is connected to them, or if nothing is connected)