I don't know if there is a free plugin that will automatically do that, but it could easily be done manually with a footer text widget. That site does not look like it is using the footer widget because I don't see the widget CSS code surrounding the links.
It looks like the theme was developed by an SEO company, so the feature may be built into the theme or a plugin that they developed. One of the plugins used is called "SpeedRealtor-seo".
From an SEO perspective it may not be a good idea. That is an old and cheesy SEO technique that may not work to your benefit.
1. When you do that, PageRank and other inheritance values do not always flow through the site properly. PR is divided by the number of links on the page, so inheritance values do not flow through a site properly when you add ton of links in the footer.
2. Footer links have been discounted for several years. This includes footer links that lead to pages within a site. Footer links are not viewed the same as a top or sidebar navigation menu.
3. If you have too many links, the site could get flagged as "overly SEOd".
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote." -- Benjamin Franklin