I'm not sure I'd apply the word "appropriate" in this context. It's not a matter of etiquette. I assume you're asking what a realistic reaction might be.
As I mentioned before, there is a huge range of realistic outcomes.
If you connect cleanly at the perfect angle with a hard kick to the fully exposed throat of someone who is on all fours and not braced for it, a very likely outcome is incapacitation or even death. Some folks might fall backwards as the guy in the video did, some might fall to the side away from you, some might collapse forward after the initial impact, some particularly determined individuals might even grab the gun, roll over and start shooting until they pass out due to a crushed windpipe.
There are guys out there who do demonstrations of taking hard directly to the throat without ill effect. It's pretty much a matter of having really strong neck muscles and being braced for the shot. Hopefully you wouldn't be fighting one of those guys and he wouldn't be braced for the shot. Still, if the guy you are fighting does have really strong neck muscles and tightens them up on impact, he might be able to absorb much of the damage if your kick didn't land as solidly as you might hope.
It's also very likely that you wouldn't manage that perfect, clean, powerful shot directly into the windpipe. Even if your aim is perfect (which would be lucky under the circumstances) , all the guy has to do is tuck his chin or shrug his shoulders or turn his head slightly, or get one arm in the way and your kick is now landing on the head, neck, shoulders, or body. In that case, the outcome could range anywhere from a knockout to no immediate effect at all.
For purposes of training, the reaction I would want would depend on what scenario I was trying to drill. If I was drilling a sequence where I managed to knock him away from the gun with my initial kick, I would have my partner react by moving back the minimum distance to where I had a chance to intercept him with my next technique before he made another grab for the gun. If the situation ever came up in real life and the initial kick worked better than that, then great! But I'd hate to count on the best case scenario and then not have it work out.