Based on the information above site #7 should be ranked #1 and yet it still manages to be placed below sites that clearly don't deserve to be ahead. Clearly there is more ranking factors than just backlinks, social media, domain age, and on-site seo as site #7 wins all these categories hands-down. FYI site #7 is managed by a large SEO agency using a very powerful network (they've bought sites in upwards of $2k for backlinks, I know because I've bidded against them and followed the domain weeks later).
So I dug a little deeper into site design and performance:
site #1 had an old crappy layout - think classic HTML with ASP
site #7 responsive wordpress theme - WIN
Page speed according to gtmetrix.com is pretty similar. - TIE
site #1: very few but more natural links, prob. all natural and a few local citations/directory types.
site #7: The usual local citations/directory w/ a private PBN network from a large seo agency. - WIN
These are not my sites so I have blurred it out. PM me is you'd like to do some analysis yourself and I'll send you the sites.
What gives? anyone want to chime in on theories why site #1 is ranking above #7?