Heinz
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The first thing I remember is that one of the players ("server") should have a static IP address (provided by the ISP for a fee).
As far as I know, people don't play "Heroes" online in its bare form, but use GameRanger, Hamachi, Tunngle, TeamViewer... Also, it is highly recommended (and more convenient) to use the HD mod.
What made you provide not a direct link to the desired page, but use this website, which has a very bad reputation? Judging by the reviews, it is often used by scammers and spammers. There are decent link shorteners, at least https://goo.gl/
I used the first link shortener.
We didn't use third-party programs to play online because we had previously managed to play online without them using the gog.com version