This trick is a "japaneese knot (or buckle)". You should at least have understood the principle of "buckle" to understand this explanation. (link in the pre-requisite tree)
For this japaneese knot, you don't surround the diabolo with the floating string, but you make the "knot" around the string on its left.
You create a "buckle" with a more vertical right stick. The floating string should fold around the left string and come back to "catch" your right stick. Somehow, you drive the end of your right stick to be caught by the string.
As the video shows, you arive in a situation where the string goes from the end of your right stick to the left string, back to the stick, again to the string and back, and again and ....
To go away from this position, simply orientate your stick toward the ground; the string will slide on your stick and the diabolo will take its normal position.
tape-tapis et Toréador