Moz Domain Authority 27

[IvanaDaulay]

Hi there, I have been reading up about Domain Authority being important to rank though I have a question about it. When trying a few google searches and using a tool to see the Moz Domain Authority i notice the following. I won't mention sites or keywords, happy to send them via private message if required.

A site ranks 1st position for most keywords including the main keyword that related to their industry, a highly competitive keyword. Their Moz Domain Authority 27, Est. Visits: 265,000,  Pinterest shares 72, Facebook shares 191 and unique domains that point to it are 55.

Yet when I look at another site, optimising for the same keyword, Moz Domain Authority 50, Est. Visits: 60,000, Pinterest shares 35000, Facebook shares 20000 and unique domains that point to it are 521.

I would have thought that the second site ranks 1st for the keyword and the first one mentioned which is in 1st position I would have expected to be on page two or three.

as I scroll down the first page for the term, all sites except for one have higher DA, visits, shares and so on.

If a high PA is required can someone help me to understand the above example? Whn a low PA site ranks much better for a primary keyword than all other sites that have a higher PA than it?