"Internet Gaming" seems to only mean multi-player gaming, at least when applied to console games. I actually have very little interest in playing my favorite Playstation 2 games against other humans over the internet. I guess it might be OK, but it isn't something I'd seek out. What I want is for my single-player gaming experience to incorporate the internet.
For example, suppose I'm playing a sports game, and the action is taking place in an outdoor stadium in, say, San Francisco. I want the game to be able to go out to the internet, look up the actual weather conditions for today, and put that weather into the game. The same idea could be applied to other types of games, like flight simulation, driving, or adventure games.
If I'm playing an RPG, the relative prices of items could take into account current real-life commodity prices. There are probably many other ways to feed real data into games in interesting ways, that could work for single-player games to "enrich" the virtual world. So I hope that game designers will realize that there are more possibilities to internet gaming than just multiplayer.