Nobody said anything about America or China. The listed uploader on the video even suggests it's from India. So quit yer trolling.
The transformers made 80 years ago were indeed dangerous. Generally they used paper insulation soaked in fire retardant chemicals.
There are a couple of observations I make about this video:
1. She's working amazingly fast and clearly with great skill. However, there's very very little time being spent inspecting the result at each stage.
2. Observe that she is holding sharp wire cutting scissors in her hand as she performs many operations on the insulating tape and wire. It would be extremely easy to accidentally nick the insulation when working at that speed. This insulation is the only barrier between your charging iPhone and the 120/240 mains voltage (or higher in a switching supply).
3. This transformer design is not the safer more modern "split bobbin" type as suggested in the original video. Instead of having a plastic barrier between two separate windings, it relies entirely on the enamel insulation of the transformer wire and a few layers of insulating tape between concentric windings. The precise number of insulating tape layers is essential to achieve the necessary safety insulation. The white tape wound along the sides is important too. Watch the video again closely. How careful is she being to count the number of layers of insulating tape? It's possible her winding machine is counting them, but this step flies by so quickly it's a bit worrying. Edit: This may be extrapolating a bit because it may be we're seeing the outer, rather than an interposing, layer of tape being wrapped in the video.
4. The transformers are piled haphazardly as they are being constructed. They are heavy and the bottom pins can have get a pretty sharp point on them. I bet some of those transformers at the bottom of those piles are getting their insulation punctured.