Question: EU anti-graft agency OLAF said Thursday it has opened an investigation into alleged misuse of EU funds in Slovakia uncovered by journalist Ján Kuciak, who was killed earlier this year. 

Source: <https://www.politico.eu/article/eu-anti-fraud-agency-probes-alleged-misuse-of-funds-in-slovakia-olaf-jan-kuciak/>

Is it all right that before "Thursday" the preposition "on" is missing?

Answer: 
There is no need for a preposition there at all, and it's not because it's headlinese. These are both idiomatic:

> 
> You said Monday that you'd have this finished by Friday.
> 
> 
> Monday you said you'd have this finished by Friday.
> 
> 
> 

You could also say "on Monday" there as well.
You can omit the 'on' if your intended readership is US (American). If you are aiming for a British readership, it is required.