From my understanding, the experiment is carried out between 2 observers under different gravitational acceleration. The first one fires 2 light pulses towards the second observer with a certain time interval, and the second observer measures the time interval between the arrival of the 2 pulses. The time measured by the 2 observers will be different. This is used as a proof for curved spacetime, as flat spacetime must give a fixed time interval.
However, if this was drawn in a space-time diagram, the 2 rays of light would be travelling at different angles, i.e. different speeds. Does this mean that travelling through the same space during different time will give you a different speed?
Also, if the time intervals are measured by 2 observers from 2 different reference frames, then why can their measurements be compared directly and even drawn into the same diagram without transformation?