We have a web application that uses several embedded Media Players. On
some workstations, such as (but not exclusively) using the Intel
82915/910GL Express Chipset, we see all the video streams overlaid one
atop the other in a one of the players, with the other remaining
black. Furthermore, all the streams are shown together in the LAST
player where an action was done (such as starting or stopping), and
the sympton is system-wide, occuring for ALL Media Player windows even
in different applications. Any idea how to solve it (other than trying
to look for more updated display drivers)?

You can try this at the cost of disabling certain acceleration done by
your graphics card:

1) On your control panel double click the "Display" icon.
2) Click on the settings tab.
3) Click on Advanced.
4) Go to the Troubleshoot tab.
5) Adjust the Hardware Acceleration slider. You can go moving the
slider 1 step at a time. A restart might be needed after you move the
slider. I'm not sure about it.

Let me know if this helped.

This sounds like a problem with the web application rather than a
device setting.  Rather then 'embed' try calling the local media
player.