Cleaning it while it's still hot is also a good strategy for pans. Obviously that has limits on how dirty it can be. But if everything went well while cooking it's fast and painless
A bit of cold water on a hot pan isn't a problem, but one should be a bit careful when pouring a lot cold water on hot pans, as they can warp
Or shatter, if they are cast iron (a.k.a. black iron).
They suggest reheating the wok on the stove, why would that imply it has to be done before eating? Does your stove not turn on after you have finished eating?
I typically wash my wok (and any carbon steel skillet) before eating. They seem to be easier to clean while hot.
But I use an outdoor butane burner for the wok, so I'm not heating it back up afterwards. I usually wash and set it upside down on the counter to drain.