International shipping services count as exports?
It's complicated, and it is supposed to depend on where the ships are generally operating from, rather than the country of the firm that owns the ships or the flag under which they are flown. Under the 2008 System of National Accounts (the international standard for calculating GDP), overseas shipping is generally to be allocated on the basis of the ports out of which the fleet is serviced. See 4.13, on page 62. The document to which it refers is the Sixth Edition of the IMF's Balance of Payments and International Investment Position Manual. You'll want to look specifically at Chapter 4, 4.131-4.136.

So if we assume that the ship owner is actually operating out of Greece, in your example he would be considered to be exporting the service for which he is paid 10 million in revenue.