The DS logic input is simply a 7kΩ resistor in series before the FPGA input (there is also a few zeners for input protection). I'm willing to bet that the xilinx FPGA's input is in the uA or greater for input impedance so it would be like having a 1MegΩ resistor as a load on the RS232, regardless not much current is flowing.
The logic analyzer then triggers a 1 or 0 whenever the voltage reaches a threshold of it's Vil or Vih specs*. The Vil and Vih are triggered when referenced to the ground of the FPGA, which is in turn referenced from the ground of the PC. The ground of the PC is connected to AC mains ground.
Ideally the DS probe would also have a grounding clip as most logic analyzers do to avoid having the thing they are measuring and the logic analyzers ground at different potentials, but if that wasn't connected, then the ground would have gone through the 9V supply or the nordic. (the nordic probably isn't connected to AC mains ground because it is most likely isolated and or double insulated as most brick/wall supplies are, the bench supply is probably not isolated unless it is advertised as such, so I'm willing to bet that your ground is going through the bench supply, you can find out by ohming from the ground to the negative terminal of either supply)
The grounding system isn't the greatest because there are loops and could be susceptible to AC mains ground noise. This would only be a problem if the ground noise got into ~50mV range which is where Vih would start to trigger on the FPGA.
*Keep in mind the ds logic isn't a real logic analyzer, a real logic analyzer can set the trigger voltage, with the FPGA we are stuck with whatever the logic levels the FPGA uses.