Doesn't this waste water? I screen-shot 7:45 of Executive Chef Sze Man Sui at Yè Shanghai on Kowloon Hong Kong.
and 0:42 of Paul Lau at Tin Lung Heen, Ritz-Carlton HK.
This appears to be a dipper well: a continuously running sink used to rinse utensils. The water runs continuously to remove contaminants, always leaving a clean supply of water to rinse dirty utensils and, in this case, to clean out the wok.
They are rather wasteful: the linked article states they use 30-60 gallons (110 to 230 L) of water per hour.
The overflowing water doubles as coolant too, these workburners put out enough BTU to heat the range to unsafe levels.
In a kitchen its all about speed and efficiency after each dish they cook they clean out the wok. Its just easier to let the water run instead of turning it on/off every min.
I want to add that these faucets provide an easy-to-access source of water for cooking. Chinese recipes often call for a small amount of water to be added to the wok during the cooking process. Given the amount of heat put out by those professional Chinese cooking stations, a few seconds to turn on the tap could easily spoil a dish (esp. stir-fries).