From what I can tell this is a list of AA newspapers in their collection. To view a detailed entry including the dates that they have, you need to go to the university catalog link given below.

Once you type in the title of the paper you are interested in, you should go to the box just below there and select the Briscoe Center for American History in the drop down menu.

You can also go a completely different route by going to Chronicling America and locating the paper there. The University of Texas-Austin seems to have their collection uploaded along with a number of other institutions--for example, one paper on the list you found, the Negro Labor News out of Houston can be found in 4 other repositories including the Houston Public Library. Also, the state of Texas has secured a grant and is digitizing their papers. Some of those selected undoubtedly will be African American; I am not sure if any of the 25 currently digitized and on the site are black papers. At this point only papers between 1860-1922 are eligible for digitization.