Right, and that's how they come to their conclusion of 'liberal media bias'. Did you even read your own study? (and by the way, the idea that the NRA is 'staunchly non-partisan' is hilarious) All things in this world are 'liberal' or 'conservative' as they relate to other entities. What their model is saying is that while the exact positions of the NRA and the ACLU are unknown, the NRA is more liberal than the ACLU. That is a preposterous conclusion, and should be sending up alarm bells for you left and right.
They are creating ADA scores for the various think tanks based on who cites them the most often. They are then using the ADA of those think tanks and looking at how often news outlets cite them. That's how they are determining the 'liberal bias' that they conclude exists, liberal meaning a position to the left of the median member of Congress. So no, they are explicitly labeling organizations as liberal based on their ADA scores. In fact, that's central to the entire point of the paper. If you aren't making a judgment on those think tanks as being liberal or conservative then you can't make any judgment as to whether or not news organizations are liberal or conservative. ie: you can't prove any media bias. This is clearly not the intent of the authors in any way, shape, or form, as they freely use their ADA scores for media outlets to label them as liberal or conservative.
Even outside their ridiculous rating system, as I outlined earlier the study has a number of glaring errors that would get a freshman student flunked such as their huge temporal issues.