The author uses "real time sampling" to acquire evolution of light intensity for one pixel at 2 GSps rate. The signal is collected for approximately one microsecond at each firing of the laser, and corresponding digital data is sent from the oscilloscope to the computer.
"Equivalent time sampling" is a different technique which involves sliding the sampling point across the signal to rebuild the complete picture over multiple repetitions of the signal.
I think parent meant that the image construction technique is analogous to equivalent time sampling. You’re correct in the mode of the oscilloscope’s use. However, the mode of the larger system is using a repetitive signal and sliding sampling points across it.