You wouldn't burn the ammonia, but use a process to 'crack' ammonia into hydrogen and nitrogen gas, for example [1]. No oxygen is involved.

Edit: Upon rereading, I found that the article actually states: "There are challenges. Burning ammonia can create polluting nitrous oxides, therefore the exhaust needs cleaning up", which would indicate they're burning it. So either the reporter misunderstood or it's really a non-innovation then.

[1] https://pubs.acs.org/doi/10.1021/ja5042836

This is the problem with lumping all pollution together: NOx is harmful to humans and animals in the short term, causing lung irritation. So yes, you really don't want a bunch of ships pumping NOx near human populations. I don't know if a ships funnel would be enough to get the fumes away from the crew of a ship while it's running in the middle of the ocean.

Excess CO2 is not especially harmful to humans in the short term (unless you are in a confined area), but it does contribute to global climate change.

Not necessarily. Ammonia burns to water and nitrogen, primarily. But the process is complicated, goes through many intermediate compounds and radicals, and won't have time to complete in a piston engine. The exhaust will therefore contain both some nitrogen oxides and some unreacted ammonia.

The good news is that catalytic converters to destroy NOx are established technology, and they happen to use ammonia as a reductant. This is definitely doable for ships, probably doable for heavy trucks, and a bit annoying for smaller cars.

Burning anything in atmosphere creates NOx emissions (really, just heating anything enough; NOx emissions from vehicles are from heating atmospheric oxygen and nitrogen, not from the fuel)

Yes, and that was mentioned in the article. I guess you need a catalytic converter or similar before atmospheric release.

Yes, article mentioned needing to manage emissions. Evidently NOx scrubbers are existing tech.