HDMI's marketshare has nothing to do with its headstart: HDMI is backed by the entire entertainment industry and was designed for televisions, while DisplayPort is backed by VESA and other computer hardware manufacturers and was designed for computer monitors.
For every computer monitor there are hundreds if not probably thousands of televisions.
HDMI's marketshare has everything to do with who the players involved are and just how much weight they have to throw around. Even computer hardware generally have more HDMI ports than DisplayPort ports.