There is definitely some subjectivity. Language isn’t something that is easily parsed and scored. That is why they give examples on the actual report about the kind of biased language they saw, or whatever other issues led to the score given.
I don’t think they mean for their website to be the end all bias resource. More of a stepping off point for you to make your own judgments.
They literally publish their methodology and scoring system.
https://mediabiasfactcheck.com/methodology/
So they do say exactly what their criteria is, and how it is scored. None of that is buzz words, it’s just a summary that fit in a few sentences. You can look at the full methodology if you want more than just that small bullet description.
I’m not saying that you have to agree with their scoring, or that it is necessarily accurate. I just think if you’re going to critique a thing, you should at least know what you’re critiquing.
Why do you say they’re opaque? They detail the history of the publication, the ownership, their analysis of bias within their reporting, and give examples of failed fact checks. I’m not sure what else you could want about how a publication is rated? I’m not saying it’s perfect, but they seem to be putting a solid effort into explaining how they arrive at the ratings they give.
That may have been the original definition, but words evolve. One of the definitions from the Merriam-Webster dictionary is ‘to cause great destruction or harm to’. So it is used correctly by modern definitions.