Vertical integration has ZERO to do with any sort of market dominance.
A company could be vertically integrated, and have a small portion of the market. A company could be a full on monopoly and have little to no vertical integration.
YKK processing raw metals and plastics, building its own zipper making machines has nothing to do with how much market share it has. It has everything to do with product quality.
Faunc is another example of "vertical integration" where they make the mills, software and controllers for their devices, as well as servos and spindles. Servos and spindles are commodity items (you can buy them cheaply from china) yet Faunc makes their own for quality and reliability reasons.