It's providing a fare in Yen because the trip originating in Japan. They provide the cost based on the country of origin.

I do this pretty frequently for trips originating out of the EU and paid against my AMEX. Typically AMEX takes whatever the daily US>FOREX conversion rate is and it shows up on your CC bill in USD. If you are subject to a foreign transaction fee, that shows up as a separate line item and is a % of the total purchase.