I looked, but didn't find, instructions for "the inbox game". I did find this
which led me to this chapter by Russell and Fisher on genre. Here's Fisher's dissertation. I don't understand it completely, but if I get it, the simulation environment used for teaching has a user interface remarkably similar to the applications inside a corporate network (calendar, some dashboards, an inbox, some documents) and there's some goal-seeking behavior that deals with this.
The game that comes to mind is Tapper.
Tapper puts the player in the shoes of a bartender. The player must serve eager, thirsty patrons before their patience expires.
Replace "serve eager, thirsty patrons" with "answer email" and perhaps there's some similarity.