He apparently holds dual citizenship in the USA and Hungary. Since the USA does not allow that, the US citizenship has to be invalid. So this conundrum seems to qualify him as a “US billionaire” per the EU rhetoric.
The US most certainly ‘allows’ dual citizenship. plenty of high federal officials have dual citizenship, you can hold dual citizenship and have the highest security clearances possible
In general, the USA allows dual citizenship; it just does not encourage it. most laws against it were struck down by the SCOTUS in the 1960s.
Regarding Soros in particular, when he was naturalized he would have had to renounce his prior citizenship, so if he is claiming dual citizenship, that would be a violation of his oath taken at that time, and that could be a basis for stripping him of his US citizenship. I have not heard that he was claiming any other citizenship, however.