A video driver is a piece of software that let's Windows interact with your hardware.
A video plug-in is just a file the program (ePSXe, in this case) uses to take care of the video part of emulation for the program.
The video plug-in is part of the program (ePSXe) itself. Your video drivers are part of your system itself.
Unless you're getting this...
...for those two lines (or if it says, say, Intel, nVidia, or ATi [there's other possibilities beyond those three] in some way instead), then you don't have this problem. Microsoft doesn't make PC video hardware, so if it says it's using a Microsoft provided driver, that means it's using the generic Windows one and your video drivers aren't installed (or corrupt and need reinstalled).
In any case, I doubt this is your problem, since the "Black screen when starting a game" seems more common. Can you run other stuff (games, if you have/play any) without trouble? If so, you likely have a different problem.
Post your plug-in settings (there's a button within the plug-in configuration to copy the data) and your PC hardware might help too (not all of it, just CPU, RAM, Video, and/or OS [though we know the latter]).
