Hmm, did they change the link? The article looks different and more in-depth than the first time I read it. I got those numbers from a separate article because I didn't see those in the original.
Not necessarily the urban population, but the cities are the focus of the claim. HUD usually characterizes urban at the county level. This doesn't necessarily match with the cities themselves. This is especially true in suburbs. I live in an "urban" county and yet my county doesn't have a large city and I have corn fields around me. It's all because there are a lot of suburbs in the county with two small cities (and a bulk of the murders happen in the smaller, disadvantaged one).
I believe that socioeconomic factors, oversimplified and summarized in my mind as a loss of hope (hope for a decent job, hope for a better life, hope to be respected/valued) are the main drivers. The claim is not that party leadership is responsible for crime, but that the policies can exacerbate it. And I don't see policies looked at here (or anywhere really).
So I believe both sides are wrong. I think it's wrong that Fox is blaming it all on Democrat policies. I think this article is also wrong for implying that policies are not a factor, focusing on only murders and states (crime in general has been a complaint not just murders, and cities were called out not states), no explanation or investigation was performed into why anomalies exists, and some of the wording seems to be misleading (why use Trump instead of governor's who actually set policy, a 90ish% increase in WY... still at the low end under 4, etc). So I feel that both sides are disconnected from what the other side is actually saying, that everyone overpoliticizes stuff like this, and that we focus so much on trying to disprove the other side (which doesn't actually happen if we misunderstand the argument we attack) that we are distracting from proving our own.