His full titles were prof. RNDr. Jiří Matoušek, DrSc; where the "DrSc" part was more than what is now recognized as a PhD. Scientific titles used to work differently in Eastern Europe.

His wikipedia article doesn't mention anything about a PhD as far as I can see, in particular it doesn't mention he didn't have one.

According to https://inf.ethz.ch/news-and-events/spotlights/jiri-matousek... he did have a doctorate.

"According to his Wikipedia article, he held a professor position without a PhD. Is that usual in parts of Europe? That seems unthinkable in the US."

https://en.wikipedia.org/wiki/Andrew_Casson

Depending on the field, it's not terribly unusual for an adjunct professor not to have a PhD in the US.

It happens in Australia, too. But it's not common.