Why do anxious people lean left?"

Indeed. The alt-right pipeline preys on fears. Gamers are afraid of losing their culture to "woke" game and anime localization, women in gamer spaces, and character diversity.

As Göring said at his trial at Nuremberg, "the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger."

The article isn't claiming that all anxious people support the left, or that all anxious people are leftists. The claim as made in the title is that "People with anxious tendencies are more likely to support left-wing economic policy," and as noted in the article this contradicts an established assumption within the political psychological community that anxiety makes people more right-leaning, because right-wing politics is based on a comforting establishment of simple, neat and objective ideals.

It's an interesting article. You should read it rather than simply reacting to an overly-literal reading of the title.