You're not considering a lot of factors that go into SEO:

1. Page speed could be better on #1.

2. Over optimization on page 2 - with many links with anchor text that includes "editing"

3. "editing" appears 80 times on page 1, 66 times on page 2, despite page 2 having more text.  I'm not saying this is a case of keyword density/spamming it, but maybe they're on the line and #2 is under it.

4. Better overall inbound link authority to #2 possibly.

5. Page 2 has repetition of both keywords in the title.  Google already punishes this if you don't have noODP by replacing your title with a more suitable one.  They aren't big fans of duplication but even so, #2 has a much different title.

6. Co-citation.  Even with a better DA and PA, the related inbound links may be more relevant to essay editing on page 1.  Also, more domains may point directly at the subpage essay-editing.html than they do the absolute page at /essay-editing/index.php

7. Analytics matter.  If #2 bounce rate is double #1, and the time on site for #1 is 4 minutes longer per visitor and they get more traffic through an email list that actually stays on site, they'd have a natural boost in the "analytics" department, as well.

There are always a million reasons why one site could or may outrank another.  All you can realistically do is improve your site as much as possible, create relevant links back, get citations that all match, engage on social and have a site that responds well when people click it.

The seo moz stats for a site is not the exactly same as what google uses to determine authority/trust so just because one seems to have more authority does not mean google thinks it is more relevant.

Hence why even some new sites with minimal back links can outrank some very trusted sites on the same topic.

Welcome to the wonderful world of seo, strap in and get comfortable because it's a never ending journey.

All the best