No. GAAP and IFRS have very strict definitions of Revenue. Transaction volume falls under the agency principle. Its not the Co's revenue.
That's not what a klarna transaction is.
Klarna pays the vendor immediately (with its credit line), and the user enters into a sort of debt contract with klarna.
Klarna's revenue is what it receives from the user.
It's a great business model when the interest rate is 0%.
As a private tech company I would assume that they are using the broadest possible definition of revenue.