There's a substantial difference between mr Lummio's approach and Canterbury's. You can easily see it, and you might then understand that the stakes in Canterbury's approach are there for a reason, a reason that is not present, or if so, to a much lesser degree, in the "original" Kochanski method, shown by Lummio.
In Canterbury's approach, which is amply unsafe, downright dangerous, the rope is wound onto alternate sides of the lever pole, causing leverage on the drum pole, making it tend to swing sideways. That's why he uses stakes to keep it in place, but bear in mind that the demonstration is done without any slope that the vehicle could slide down. Hence the vehicle will stay more or less in place when tension is removed from the line.
The Real World often is a bit different. The Canterbury drum pole will swing swiftly and remove those stakes in a jiffy when the vehicle slides back down a slope. It may also sever the legs of the operator when it swings back.
Kochanski and Lummio wind the two parts of the rope neatly side by side, never causing much sideways leverage on the drum pole. Both parts are essentially in line, as seen from above, never at a large distance from each other, as in the Canterbury application. The distance between where the rope is attached to the drum pole in Canterbury's approach is a major flaw, and the method should not be used in that way.