I don’t think the author is wrong, except in how big the problem is.
I don’t think the illiberal left is as big of a problem as the right. In fact, I think the views on the right about creating legislation to oppress women and minorities is a mainstream view on the right that has probably made it into their Supreme Court. While the illiberal left remains a fringe movement that is more of a distraction than any sort of threat.
I think yeah the far right probably has more sway in government at least in North America, while the far left has more cultural influence, through mass media, education etc.