This case was not filed by any country, it was directly filed by Karim Khan, an employee of the ICC.

The court that requires a country to file is the ICJ. Iran is already a signatory to the ICJ and there is nothing that would legally prevent them from filing a case if they wanted to.

I was also curious about parent's claim so I did some searching of my own. The claim is from a report published a few days ago called 'South Africa, Hamas, Iran, and Qatar: The Hijacking of the ANC and the International Court of Justice':

https://isgap.org/follow-the-money/

Its author, the Institute for the Study of Global Antisemitism and Policy, is ostensibly American, although I can find no indication of its incorporation in the USA. The Israeli government is the largest donor to the organization according to 'The Forward', which is a newspaper incorporated as a non-profit charity in the USA.