The starch granules in the noodles absorb water and swell when heated, a process called 'starch gelatinization'.
Starch granule gelatinization.
Taken from "Starch gelatinization and its complexity for analysis" (paywalled).
Starches are made up of of amylose (long chain sugars) packed very densely as crystals. These crystals loosen during gelatinization, and when given sufficient heat and water, completely burst and disperse their amylose. Point 4 represents where the granules have hydrated to point of bursting, and the amylose begins 'leaking' out. Full dispersion is the end goal of using starch thickening methods, like slurries or roux, but very much unwanted for noodles. The temperature at which the peak at 3 is achieved, and overall shape of the graph, varies depending on the amount of available water and type of starch.
Ideally for chow mein, the noodles will have starch granules evenly and fully hydrated as well as intact, shown in the range between points 2 and 3 on the graph, leaving no rigidity, grittiness, or powdery texture from under-gelled starch in the final dish. These types of noodles typically rely on wheat protein formed during kneading or added egg protein to maintain their structure, and generally have a high degree of hydration uniformly throughout when fresh.
In contrast, dry noodles have a gradient between points 2 to 4 - under-gelled core with al dente texture, partially dispersed exterior - due to gelatinization being dependent on hydration, and rehydration progressing from the exterior to the core. . Dry pasta noodles benefit from this for sauce adhesion, but the dry hakka noodles you are boiling would be easier to work with if they had the properties of fresh noodles above.
The recipe you provided with the 30-second boil, 2-3 minute soak for dry noodles gave poor results because of continued gelatinization during the stir-fry phase. The reintroduction of heat, as well as water from the vegetables and the noodles themselves, will cause fully cooked noodles to cook further, resulting in amylose dispersion, resulting in loss of structure (mushiness) and increased viscosity (clumping).
@unlisted was completely correct in the instructions provided and assessment of your recipe video, and as you described, the instructions provided resulted in par-cooked noodles after boiling - this is desired, especially in a domestic kitchen with lower stove power output.
For better chow mein noodle cooking technique, refer to these videos:
The first video follows the same process in the recipe you provided, but note that at 02:15, when the noodles are added and tossed, a large amount of steam is released. High-powered commercial wok stoves output heat in the range of 30,000W, allowing the water to very rapidly evaporate and not remain trapped to steam-cook the noodles. In contrast, domestic stoves output heat in the 1,500W-3,000W range, making stir-frying more akin to stir-steaming. To compensate for this par-cook the dried noodles, even less than al dente and just enough to soften them, to achieve the target texture during frying.
Lau's recipe is done on a plug-in induction stove, most of which max out under 2,000 W. Hydration is controlled by steaming the noodles instead of boiling, and only submerging the noodles in hot water for 15 seconds. The noodles are then fried first, and alone, to crisp and prevent added moisture from continuing gelatinization. Only after the noodles have finished becoming crispy are the vegetables and other wet ingredients added. Fresh noodles are used, but dry noodles are also accounted for - boil according to directions, or increase steaming time.