Hi everyone here!

Firstly background:
1) Every dosbox related game in GOG has each lunch configurations. For popilous they are:
a) dosboxPOPULOUS2.conf.
b) dosboxPOPULOUS2_client.conf.
c) dosboxPOPULOUS2_server.conf.
All three files should be found in game installation directory.
2) This configuration usage defind in your link as 'Target' property.
You can find example of how it works in dungeon keeper multiplayer tutorial, here on GoG (not able to add links, sorry).
So now to run multiplayer you need
1) Define correct traget props.
For server: change link target prop from dosboxPOPULOUS2.conf to dosboxPOPULOUS2_server.conf.
For client:
a) Open dosboxPOPULOUS2_client.conf in any text editor.
b) In [serial] section change serial2 value to the nullmodem server:%SERVER PLAYER IP%.
example: serial2=nullmodem server:101.102.103.104.
c) Replace [autoexec] with the next text:
mount C .
c:
Pop2 /ss /h
exit
d) Save dosboxPOPULOUS2_client.conf changes.
e) Change link target prop from dosboxPOPULOUS2.conf to dosboxPOPULOUS2_client.conf.
2) Firstly server should run his game.
3) After some delay(to be sure that connectivity possible), client should run his game to.
4) In two player menu one of you should defined hisself as good, and other as bad.
5) Select serial as connection type(connect serial), and model 2(should be defined as default so changes should not be necessery) and push connect button.
...
6) Profit! Multpiplayer runs for you!

About possible questions:
- While 2-nd player not connected errors should be received. This is OK.
- 2-nd Player will watch ???? in connection menu. This is OK.
If anyone will have futher questions: please do not hestitage to ask me.

Does using the tools located in the Start Menu Folder (Graphic Mode Setup and Run Multiplayer Game) for Populous 2 do the same thing?

I tried using them and your method but the test computers are not connecting to each-other.