I don't understand your objection at all. They clearly break out "Gross Bookings", which is the total of all fares, from "Net Revenue", which is the amount that goes to Uber after paying drivers. The income statement is very clear in that respect.
Bookings would certainly be a key financial metric... and would certainly belong on a financial statement since the funds transit Uber's books before being distributed to 3rd parties.
Transaction volume is an important metric for tracking the growth of the business, but it is not revenue.
The fact that the funds go through Uber's account has nothing to do with it.
See Uber's terms of service:
"with respect to Third Party Providers, Charges you incur will be owed directly to Third Party Providers, and Uber will collect payment of those charges from you, on the Third Party Provider’s behalf as their limited payment collection agent"
Bookings are not revenue, which is why Uber can't call them revenue, but then wtf is "Contra Revenue" and how does Bookings - Contra Revenue = Net Revenue?
You may think this, but coming from an analogous business I can say virtually all "middlemen" market-making companies (think online travel agents like Booking.com or Expedia) track like this: start at the top with Gross Bookings, then make a bunch of deductions to Net Revenue. And in truth it gives a more accurate picture of the business, because the "Take Rate", that is Net Revenue/Gross Bookings, is an important metric in and of itself.
I think you are confusing the data presented by WSJ with an audited SEC financial report. Uber didn't make anything public - this is just data they presented, privately, to their investors who obviously know the difference. I mean, this data was leaked to WSJ.