xlink kai, Hamachi and things like that rely on the games having the option to play over LAN -- all such services are is a VPN (a way of sharing private networks over a public and untrustworthy one like the internet) with a nice frontend that saves fiddling with VPN software and allows a measure of matchmaking. For the Wii that amounts to two games with such functionality according to
http://www.co-optimus.com/games.php?system=3&lan=true&playerCount=2&countDirection=at least
The link is not so reliable but I would not be surprised if I could count the whole list off on one hand. There are a few more on the xbox, xbox 360 and PS3 as well as the PC though even there such things are getting less common as time goes on.
This then means somewhere out there on the internet is a server that your device speaks to and it sends things around to everybody. Some of these servers are just things that rebroadcast to others in the game, many more servers do a lot of things behind the scenes though and this is what people have to emulate. Emulating these servers is not commonly done, especially not on consoles and it gets even harder if you do not have a working server in the first place. This means when the server dies then so does the multiplayer, sometimes a company will donate the source code