Kay is the editor of The Walrus and has been writing about Uber, usually positively. But here, he argues that it's unfair for competition from Uber to undercut the taxicab monopoly. He could have gone two ways: (1) advocate banning Uber or using tax money to compensate taxi monopolists whose monopoly power is weakened by Uber or (2) say that even if doctors and lawyers scream bloody murder, they're wrong because they, just like taxi cab monopolists, don't deserve a monopoly.
Unfortunately, he chose (1).
Kay does make a good point and it's one that the late public choice economist Gordon Tullock made in a famous article titled "The Transitional Gains Trap." Tullock pointed out that although many economists can agree that it's inefficient (and, I would add, wrong) to give monopolies or subsidies to various industries, after those monopolies and subsidies have been around for a while, many of the "gainers" are people who paid for their gains.