When my Mathematica browser plugin opens the CDF player, for example to play a Demonstration from the Demonstrations Project, I get this new icon in my dock:
I assume that this is the CDF player icon.
Right clicking this icon shows the New, Open, and Documentation Center links:
A developer straightened me out on this. Formally, this is the “FrontEnd as a Service” icon which the browser plugin uses.
The pop-up menu, if any, should be empty.