The whole site (including LGBT News) is built from scratch, using PHP and MySQL. I came across a few turnkey Hacker News sites, but didn't really like any of them. I decided to build LGBT News from scratch just because I thought it'd be easier to integrate into the existing site, and I thought it'd be a fun project (I usually tend to do that for the learning experience).
Login uses Facebook Login (which has been a huge headache), countries and regions were implemented using an ISO database, and some of the additional data (population, religions, etc.) comes from Freebase.
I created LGBT News because there was a lack of other information outside of the actual laws in each country and region. When you visit Russia's page (http://equaldex.com/region/russia), you might assume that it's a little more LGBT-friendly than it is, but if you see some recent headlines about LGBT rights in Russia, it might give you a totally different impression.
When you submit news to LGBT News, you tag it with a country or region so that the news is then surfaced to that country's page.