After reading that link, and checking the "See Also" section at the bottom, I found out a few interesting things that I was unaware of.I think Sega might disagree with you again!
http://en.wikipedia.org/wiki/Sega_Channel
I'm not sure Sega channel had multiplayer, but it brought the console online to download new content and predated many others.
I will agree that Dreamcast made it viable and then it became more wide spread with PS2 and later Xbox.
First, it appears that the 2600 was truly the first console to have online functionality. With the GameLine adapter, you could download games to play right on your 2600. No multiplayer, but still, it was connected.
http://en.wikipedia.org/wiki/GameLine
The next apparently was the Intellivision PlayCable. This used a connection with your cable service and could also download games to be played on the console.
http://en.wikipedia.org/wiki/PlayCable
Apparently the PlayCable was introduced in 1981, with the GameLine coming some time before that, though I can't seem to find a date. Either way, it would appear that these 2 machines, as crude and rudimentary as they are, were in fact, the first consoles to be "connected" in some form.
The other interesting fact I learned was that there was a modem available for the Nintendo Famicom. This was well after the 2600 and Intellivision, so obviously not the first...
http://en.wikipedia.org/wiki/Famicom_Modem
But after reading that, I realized something quite amazing. Since the original Famicom had an available modem, that means that EVERY SINGLE Nintendo home console ever released, since back in the 80s, has had some form of online connectivity. Granted, this has never been GOOD connectivity, but still. That is a long time making hardware, and every step of the way, they have tried to do the online thing. I found that pretty interesting.
Other than the Wii, here are the other 2 parts from Nintendo...
http://en.wikipedia.org/wiki/Nintendo_64DD
http://en.wikipedia.org/wiki/Nintendo_GameCube_Broadband_Adapter_and_Modem_Adapter