Settlers 2 is actually a somewhat older DOS game, which has been redesigned by some motivated programmers and is now also available in the 32-bit version for MacOS and Windows, as well as in the 64-bit version for Windows, and also plays decently via the Internet.
The Settlers II Gold Edition is still available at GOG.
What I remember is that RTTR requires the Gold edition of the game.
It's definitely possible to play on LAN. We've played it before. Somebody else will have to clarify what you have to do to be able to play it over the Internet.