That is a very good point. I researched about it. It seems they do have to treat and recycle a lot. Below is an article published in Jan 2019. 

“Due to the efforts of highly trained waste management professionals onboard, some cruise ships repurpose 100 per cent of the waste generated onboard — by reducing, reusing, donating, recycling and converting waste into energy.

“Cruise ship waste management professionals recycle 60 per cent more waste per person than the average person recycles on shore each day. " “Cruise lines recycle 80,000 tons of paper, plastic, aluminium and glass each year.”

Looks like this is the answer. May be Peter can shed some light.