"nobody has time to think about sinking qi."
Yes, that's true. Just as no one has time to warm up or stretch before they are thrown into a fight. It is a little bit interesting to compare our practice with a musician. Think about a violin player who spend
a lot of time to warm up before every concert. They must do this, otherwise they can not control the instrument sufficiently. When you practice a martial art, you have a lot of time to prepare yourself if you enter a competition or have a sparring session, but when it really matters, you have no chance to prepare yourself. You must reach to a point where you can switch on and of what you need just like you switch on and off a light bulb. Well, it's obviously much more easier said than done. But with that said, I think that "sinking qi into the dantian" should more be considered as an ingredient of body mechanics. You need to use your body as a whole, and the center for this whole is somewhere in the stomach area, call it whatevah you wish. As when you punch, it is pointless to merely "think" or try to imagine your qi sinking down to the dan tian. Instead, we must learn how to use this area in a most active way, incorporate the "sinking" in the very physcial action. Then, as you practice over and over again, this "sinking" will become the most natural part of your body mechanics, so you don't even need to think about it when you punch.
btw, in an earlier discussion someone said that the guy in the clip was a trained guard...