Let's just read the title: "As unions decline, inequality rises"
That is very much a statement about correlation. Otherwise it would say, "Unions' Decline CAUSED Inequality". But, to anyone with a passing knowledge of statistics, that is clearly an impossible claim to make. This is one time series realization for one country.
Let's go further. Is there any mention of causality in the article. And I do mean quantified causality. The answer is "no". Is there even any mention of correlation? Again, the answer is "no".
Let's keep going. Let's evaluate the aims and intent of the article. Let's start with EPI, the publisher of this article. The Chair of EPI is "Elizabeth H. Shuler ... president of the AFL-CIO, a federation of 58 unions and 12.5 million working people". Other board members include current and former union leadership from the United Steelworkers, the UAW, the Nonprofit Professional Employees Union, Service Employees International Union, the International Association of Machinists and Aerospace Workers, the American Federation of State, County and Municipal Employees, the Communication Workers of America, and the American Federation of Teachers. All huge unions.
In other words, this publication is not a work of science. It is not a credible academic publication. It is the motivated, self interested rhetoric of union leadership.