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

Do the heroes really need a registry entry? It seems to work fine without installation...

So what if it works without installation? The standard HoMM3 always needed a registry entry.
Now, HotA, ERA, and MoR have been detached from the registry.
And the HD mod also loads settings from its own ini files, and this applies to SoDa as well.