It would be nonsensical to state numbers for the total number of people can who move through an entire city because it is heavily dependent on how much space is dedicated to each mode of travel. They are making a comparison of how many people who can move through a given amount of space depending on what mode of transportation they are using.
The figure of 25,000 people/hour in buses makes sense to me in a city like L.A. This is where I'm taking issue with the whole article, their basis for analysis is apples-to-oranges.
If you look at the sources I linked they give the estimates of 1900 vehicles per hour as the theoretical maximum capacity for a lane of traffic, 30k people per hour as the maximum capacity for a single subway line and 10k people per hour as the maximum capacity for a 2.5 meter bike path.
Those are all pretty close to the numbers they gave for each mode of transit, so it seems reasonable to assume that they are basing their numbers on something similar to that. That is an apples-to-apples comparison because each of those things takes up very close to the same amount of space.
I read your sources. Your source, in particular the 1900 cars/lane/hour specifically illustrates the poor quality of this article, where the author tries to take us into an alternate universe where the theoretical maximum flow of passenger vehicles is 1600/CITY/hour.