Looking at the video, I would say he's using a variety of soy sauces, with one or more being a dark or black variety.
Traditionally, the cooking is done over a charcoal stove, giving the dish a distinctive flavour. Some places serve it with dark soya sauce and also dried salted fish.
Also from Wikipedia, a picture of the dish with dark soya added:
Update as per the edit to the question:
Dark and black soy sauces tend to have a thicker consistency than 'regular, everyday' soy sauces. (And some are sweetened.) The viscosity allows the sauce to adhere to foods more easily and creates what I refer to as a lovely sheen.
From Serious Eats:
Dark and Double Dark: Like Japanese dark soys, Chinese "dark" soys are darker in color and thicker in texture, but tend to be lighter in saltiness. They are generally fermented for a longer period of time than their thin counterparts and often have added sugar or molasses, giving them a sweet-salty flavor and viscous texture. They are used solely for cooking, often added at the last stages to season and add color to sauces.