I always thought hydraulic pumps were high precision.
They are relatively precise. Those old machines can turn out very good work in the hands of skilled operators. The workers appeared to be very adept at their tasks. We were not shown any of the inspection processes in the video, except where the guy "tested" the fit of the bearing block into the pump body. The jigs and fixtures were simple and effective. LOTS of good, highly precision, parts have been made on manual machines for over 200 years, before CNC came along. The industrial revolution began in Britain in 1760.
Would that be a "forged" aluminum pump body since they "pressed" the not fully solidified aluminum into the mold?
I never tried that with a casting. But it is an open casting and you would at the very least potentially push out any bubbles. The permanent die will give you less chances for cavitation. But that is part of the melt, the temperature actually. Too hot and you have a lot of hydrogen bubble formation in aluminum. When I started casting as a 13 year old I made quite a few swiss cheese castings thinking hotter was better.