I asked my friend and former shuttle FDO Roger Balettie about this, he kindly gave me permission to quote him
..those are "Eidophor" displays - similar in nature to the much larger
versions back in the Bat Cave behind the 10x10 and 10x20 front
displays. They were used early on in the Shuttle Program for the FDOs
to have clear overlays to put onto the projected ascent and entry
displays put onto those two GIANT round monitors. I remember seeing
several FDOs having grease pens and marking the overlays up to
identify certain abort boundary call marks, or other important events
on the trajectory. Then, as the mission events unfolded, they could
easily see their real time data and these easier-to-modify overlays
together.
During orbit phases, we just used them as regular displays - giving
the FDO and TRAJ together 5 total displays to have up. Plus, as you
can see, the top of the display case was excellent real-estate for
storage. 😀
Roger's website about space, being an FDO, and the Trench is here: https://balettie.com/space/