The point by the parent is that Chrome was a moat (as was Android, that's why they bought it and pursued mobile in the manner they did; Android was a subsidy program to protect the search monopoly moneymaker), which Google used to ensure the position of search, to ensure that search was unassailable by competition. In the case of Android, Google was terrified of being leaped or replaced in the shift to mobile, inflection points in the landscape are when monopolies in tech are at their most vulnerable. The parent's point was not that search wasn't already dominant, it's that Chrome helps to protect that dominance.

Microsoft used the exact same tactic repeatedly. It's one of the cornerstones of any dominant corporation, to build and leverage moats to keep competition at bay.

Google had 61% of the search market in 2008. Google used their free browser, paid placement deals, and acquisitions to further enhance their position to the 90%+ that it is now.

Why do you think Google bought Android? Google panicked after seeing a private demo of iOS. Remember, back then Google execs were sitting on the Apple board.