Just a wild guess but maybe there are two isolated grounds on the PCB. Also, this forum is not necessarily for circuit-technical questions. It's pretty much for CircuitStudio-related questions.
Your question came through on main Forum Stream too so there is a pretty good chance that someone smarter than me will respond. What makes you think that both sides of the capacitor are connected to ground? Try putting an ohm meter across the caps and see what it says. Most of the time these capacitors are not marked well. If you really needed to know the value I would remove one and test it with an LCR meter.
So judging by their location right next to connectors and that there is one each side of the board and they connect to an exposed copper area running around the perimeter of the board, presumably for an electrical connection to a chassis that fastens around the board, I would say they are likely AC coupling between the chassis ground and the main ground of the circuit so they are connected as far as AC signals are concerned but they remain isolated as far as DC voltages are concerned.
If the ground traces are too thin, maybe the designer wanted to reduce the AC impedance without creating a DC ground loop. If there is no value, it usually means the designer wasn't sure what value would work best. The designer may have wanted the option to replace the cap with a short or simply leave it unpopulated to see what worked better.
I could be wrong, but I doubt they are. Are you using a multimeter in continuity mode to 'ring out' the connection? If so, check to see what resistance and below will ring. I've used meters that ring anything below 500 ohms, which usually rings on power to ground connections.
It's just to get rid of any static charges, when the board is inserted into the chassis. This is because the edge is going to be the first bit that touches the chassis, and the capacitors have physically been placed with one end close to the chassis, and the other end connected to the PCB ground. As rachaelp says, its for the AC signal, that brief spike and then in theory the board ground and the chassis ground should be at a closer potential. Sometimes there is a parallel resistor too (>1M), to provide a high impedance DC path. In the duplicate thread (which makes it awkward to provide a good response, because it is only by chance that I saw it), it showed the portion of the schematic, with the ground connection on each side. However, it should have been drawn better, with a different symbol on each side to show the difference between board ground and chassis ground.
