The report says that a mid-sized cruise ship can use as much as 150 tonnes of fuel each day, which emits as much particulate as one million cars. Is that right?
That's correct. And the reason for this is that their engines run 24/7. Even if they're in the ports, they have to keep running their engines, because it's not only a transport mode, it's a hotel facility. They have a spa on board, restaurants ... and that needs a lot of energy — more or less the same energy a mid-sized city needs.
The density of gasoline ranges from 0.71–0.77 kg/L
524 gallons is 1983 liters, giving 1407 kg/year, or 3.857 kg. Thus, if a cruise ship burns 150 tonnes a day, it burns as much as fuel as 38k cars. Only if a cruise ship produces 26 times as much particulates per kg fuel would this make sense.
Also, the claim "more or less the same energy a mid-sized city needs." is quite questionable. If we says that a "mid-sized" cruise ship has 3k passengers, and a "mid-sized" city has 100k population, then this would mean that a cruise ship is providing 33 times as much energy per person as a city. While it makes sense that it would be higher for a cruise ship, 33 times sounds rather high.
There is this, however:
Large ships run on heavy fuel oil, which is legally permitted to contain 3.5% sulphur – that’s 3,500 times what is permitted in road fuel. In EU ports and waters, ships are legally required to switch to a cleaner diesel, but even this, capped at 0.1% sulphur, is allowed to contain up to 100 times more sulphur than road fuel.
So, it appears that are particular types of particulates for which a cruise ship produces as much as one million cars, but the article is poorly worded in implying it is the amount of fuel, and the constant running of engines, rather than the different fuel composition, that causes it. Note also that if cruise ships were not burning this heavy fuel oil, then either it would be burned somewhere else, or not use at all, and the latter would be rather unlikely.