It's not about who invented a thing, it's about who perfected the thing.
Did you know that some ancient Greeks actually invented
steam engine? Should they get credit for industrial revolution? No, because they saw it essentially as a gimmick or a party trick. Like @Cajoes mentioned above, their democracy was also drastically different from ours. in Athens, poster-boy for democracy, only 10-20% of people could vote (and certain people today would find especially problematic that they were all men.)