Wow. She is fast.
Andy_C: but her windings ARE flat and parallel. Watch closely. She's laying two wires, bifilar wound. She uses the tendency of the wire to space itself, does one layer then runs the second layer back the other way.
The leakage inductance - I'm pretty sure is a function almost entirely of the ferrite core geometry and gap, not the windings. Anyway, bifilar winding. Best possible coupling.
Psi: the twisted wires will be soldered with an iron, the ordinary way. Can't recall just now what it's called, but the enamel will be a kind that decomposes at soldering temperature, and also acts as a soldering flux. It works very well. Just wrap the enameled wire round the terminal, apply heat and solder. Perfect joint.