The opening of Kwang-Gae is similar to the opening of the kata Kushanku. But when we circle our arms low, in Kwang-Gae we perform closed ready stance B, whereas in Kushanku the hands come down in front of the groin.
One of the applications for closed ready stance B is a headlock. So if we use the heaven hand to block a right haymaker, we may then strike the opponent's neck (the splitting hands) and then try to wrap our right arm around the opponent's head, placing them into a headlock as shown in the combined gif below.

You can perform this with or without overhooking the opponent's right arm.
We then apply a guillotine choke. Grab and pull in the opponent's shirt with the pulling hand while squeezing their neck against your right side with the upset punch. This is why the upset punch is performed in slow motion, to indicate either that the technique is difficult or an unusual application, not that you would perform it in slow motion against a live opponent! Usually for a guillotine choke your hands remain clasped (see the example below) so I assume the pulling hand is performing some assisting function such as pulling in the opponent's front shirt to keep them lowered.
| MMA teacher miming the guillotine choke (left) as a close uppercut motion. The guillotine choke may also be done while overhooking the opponent's right arm (right). Source: HowCast |
Given the follow-up movements provided by the pattern (e.g. the next set with the palm hooking block may be used as a reverse head throw), I suspect we are intended to overhook the right arm so that we still have control if the opponent backs out of the headlock.
But Does It Work?
Although this technique is taught in some self-defense and karate circles, I've read criticisms from wrestlers that no one will just let you lower their head like that. A guillotine choke is usually applied against an attempted tackle, because the opponent's head is already lowered.
This makes the technique somewhat opportunistic. If striking the opponent's neck with the splitting hands causes the opponent to lower their head, then a guillotine choke is appropriate. If they do not lower their head, then the pattern provides other options (additional strikes to the neck, a knee to the groin, etc). Additionally, the pulling hand and the drop into front stance may used simultaneously to pull down the opponent's front shirt, lowering their torso.

















