You need a higher frequency, but you can generate that with one of those ZVS induction supplies China is cranking out these days. YMMV what supply voltage and work coil you need.
The power supply in the video is probably delivering a few kW, but the efficiency will also be poor with that one-turn coil. A soldering iron at 60W (and better efficiency) would still be able to do that joint, given perhaps a minute or two of heating time (and if you didn't mind having a blob of solder on the outside). Probably 200-600W would be adequate for a reasonable production rate, and with a tighter fitting coil.
Tim