It may have won the market by default, but it took very good advantage of the opportunity that landed on its lap by investing heavily in developing excellent IP and relationships with partners.
There is always a "luck" element to any sort of success; it's how one takes advantage of the lucky break that really speaks to the quality of a company's management team, IMO.
ARM is a good, well run company that has ridden the mobile bull to very nice profits for its shareholders. What more could ARM have done to take advantage of the "gift" that the universe gave it?