Many anarchists criticism of private property rests on the idea that it is the root cause of the capitalist’s legal right to appropriate the fruits of their employees’ labor.

This is the Marxist analysis (as also pointed out in the article), not one commonly shared by Anarchists.

I don’t think the argument in the article is particularly new or enlightening, and in fact the proposed democratic company is apparently modelled after Mondragon, which was founded on Anarchist ideas nearly 70 years ago.