Hm then, we wont see each other when playing ?
No, for all practical purposes, it is the exact same as being on Battle.net without the restrictions of submitting to Blizzard's normal multi-player standards. For instance, when you play online you don't actually see another person moving their mouse around, ordering units and sitting plugged into your computer. The way a multi-player online game works is simply by creating an instance of a game for the 'host' (because it's peer-to-peer, one person has to have the original game, or in this case the 'host'). While the game goes on, each computer relays information about what each player wants to do with their units to other players, and that gets executed for other players on their screens as well.
In layman's terms: If we play a game on battle.net, I'm not imputing commands directly into your computer, I'm doing things on my own computer. When I order my men, your computer copies the command like a mirror. You're technically only seeing and interacting with the mirror image of my units, but since when you affect the mirror it affects the real unit on my end, for all intensive purposes you are -really- interacting with me. The chat system in game works just like an instant message (which functions in the same basic way). I'm not typing the message into your computer: I'm typing it on mine, then it copies that message and sends it to you, then it displays it for you. When you respond, the same thing is done: the message is sent to me so I can read it.
The reason it is done on single player is that the single player game automatically assumes there is only one player (which is technically true, it just so happens that another player is allowed to command the "computer's" units via orders being sent to them through the computer). As a result, since the other players aren't actually "players" as defined by Warcraft III, you can have as many players as you want, since all you have to do is choose a different set of units that that "player" is allowed to issue order for.
Still don't understand? Feel free to ask, and I'll try to explain again.