The contact page at the demo is nothing but a normal static page which uses a map shortcode, some content, and a contact form generated by a plugin.
You can use any of these three plugins, all of them are compatible with Higgs:
Adding a map at the Contact page
Provided that you have successfully downloaded and installed the StagTools plugin, you can easily use the shortcode generator and generate a Google Maps shortcode. You will only need your location’s latitude and longitude.