This works with the sample principle as the "Inexhaustible Bottle" or "Magician's Water Pot" tricks (and similar). Pascal's law is the driving force that makes it work.

Wikipedia has a pretty good description of it.
https://en.wikipedia.org/wiki/Inexhaustible_bottle

The pump would probably be used in a horizontal orientation with cupped glass opening placed around the nipple. The pump (the handle is at the top in the pic) would be pulled out and pushed in to create the suction action. (Modern breast pumps create a suck then release action, like a baby would.) The milk would be collected in the side of the glass bowl and then could be poured out. It looks like the nozzle of the pump is curved so that it could point up during use to keep it out of the collected milk. It would probably work.