Uber is not a two-sided market place at all. Two-sided market places are characterised by increasing gains from size, because it improves the functioning of the marketplace and discovery.
For ride-sharing businesses, this is only true for very small sizes, as they grow the size of the platform doesn't deliver any significant additional returns, whether you wait 2 minutes on uber or 3 minutes on left is largely immaterial. So its an asymptotic marketplace, which is vulnerable to competition.
Even the characterisation of a marketplace is dubious because there's no price discovery between drivers and customers or much other interaction, it's more like a matchmaking site, so there isn't really a lot of unique features to differentiate one from another.
Thanks for your new definition of 2 sided markets that excludes Uber. Maybe you should write for the Economist instead of hacker news.