Jan Kuciak (an investigative journalist) and his fiancee were killed (2 shots in the heart close range and then, bullet in the head while kneeling respectively).

At the time he was investigating the connections between the current government and mafia. It triggered huge protests in Slovakia. The prime minister of Slovakia was forced to resign.

Marian Kocner is a suspect of ordering the murder. Apparently he was using Theema to do that.

If it's true I'm really curious how they did this. Probably they got the private key somehow?

They could receive the private keys from Theema directly, but they also have access to Kocner's phone so they could extract it from there.

This is an investigation of high-profile murder so I assume they have resources to do either of these.

They did not break Threema's encryption. They simply extracted the database from the unlocked iPhone of the target person.