You have the gist of it. It's basically saying we'll partner with you and publish your game.
Is this legal? Of course. There are companies are are "Publishers" that partner with developers and help sell/promote their games and offer other services.
For example, take Angry birds for example. Rovio made the game, and chillingo sold it, and helped make it a success.
You've probably heard of these publishers before. Some of the big ones are EA Games, Atari, Activision, Sony, Microsoft.
And finally, no we wouldn't publish any app. That's part of our terms of service is more there just in case we do launch a publishing service, or were to partner with a user who has a game that could use our help.
We'd approach you about the potential publishing deal, if one were to come up.