As you may suspect, much has changed in the past 9 years for SEO.
Technically, the TLD doesn't matter. In practice, it matters indirectly. You'll find the .edu sites tend to be authoritative as the university has strong domain trust and authority. Getting .edu links will typically improve your site on both measures. With that said, I know there have been sections of .edu sites (especially student-created sites where some students were selling links) that have been penalized by Google.
There have been some TLDs, like .info that were preferred by spammers because they were being sold for $1 or $2. It's possible Google could use a TLD to determine quality, like .com vs .info, with some triggers to bypass those rules (like a .com with 0 trusted backlinks or a .info with a million), but it hasn't been proven (though correlation data might suggest so).
Another aspect of TLD is if you run a non-.com domain, the .com version of your site is likely getting accidental links and visits. Accidental links occur all the time, even on the most-respected publishing sites. It's always best to get the .com if you can afford it.
As far as DMOZ goes, the Yahoo Directory was closed a couple years ago and DMOZ finally shut down in March of 2017. You can thank AOL for mismanaging it.
Good question. I am also curious about all the new top level domains (.tv, .shop, .me, .io) and how back-links from them are ranked? Are they all treated the same? I'll let the SEO experts answer as this is above my pay grade!