Yes, the sound is the hydraulic PTU running as the hydraulic pressure in the Green and Yellow systems decays. It is fitted in the main gear bay area and runs one way or the other to support the pressure in whichever (Green or Yellow) system has the lowest pressure. It cuts in and out at certain pressure drop values* with some hysteresis applied. However, the PTU in that you-tube clip (#3), seems to be cycling excessively. I wonder if the various hydraulic accumulator charge pressures were correct?
As to why they don’t use an electric pump instead of a PTU; well there are electric pumps in the Blue and Yellow hydraulic systems, and I dare say there are redundancy and diversity considerations for having a mechanical instead of electrical back-up in the event of certain failures, such as Emergency electrical config, where electrical power might be very limited or absent.
*Cannot remember the A320 figures, and can’t be bothered to look them up!