Wikivoyage uses multiple map types; a static map which is created manually and a dynamic map which is generated from (lat, long) co-ordinates and OpenStreetMap base maps.
This website uses the Wikivoyage API to get and display all the information you see. This is the MediaWiki API, which is a general API for accessing data from Wikimedia projects. You can find information about it here: MediaWiki API.
