It looks like an open die hot forging process.

What's interesting is that they've mechanized the hammer part but rely on muscles for the positioning.

In contrast modern hot forge work has powered manipulation but it's still the same process. for example here: https://youtu.be/YobXFODkp50?t=2m3s .

Update: I checked in with my Dad, the metallurgical engineer.

• He says that it is a hot forge process but very poor safety equipment.

• The stuff that they are throwing on it at the beginning may be graphite lubricant to make the dies last longer. It may be water/graphite mix which would also tend to break off surface scale.

• The part where their brooms are catching fire (around 1:00) is because they are sweeping the scale off the die. You probably want to avoid pounding scale into your product. He wondered how long brooms would last.

Second update, I asked my Dad for more details.

• Revisiting the movie it looks more like there were taking a full sized ingot (for that time) hot forging it down for a big motor shaft. Note the tapered side on the product they start with. The movie was filmed in the former Westinghouse's East Pittsburgh plant which is about a mile away from (place my sister works).

• I would suspect Westinghouse was using open heath ingots from neighboring Carnegie (later named U S Steel) Homestead Works and possible alloy steel.