Almost all shipping by weight is done by burning bunker. By ship quantity, most ships probably actually just burn some variant of diesel. Some do run off natural gas.

If you read through industry journals, you can find some point in the late 80s where the industry journals were all reporting about how all ships would need to go back to burning coal soon. I'm pretty sure this was just a fantasy that shipbuilders paid the journals to push as it would mean the opportunity to sell lots of new ships.

I doubt the statement you quoted is grounded in any reality.