The Craig Retroazimuthal (aka "Mecca") projection.  Centred on Makkah, you can measure the great-circle azimuth <b>to</b> Makkah from any other point on the map by measuring the angle from the vertical.  Like all retroazimuthal projections, distortion is high near the edges, and there are unusual "wrap around" effects, seen here as an overlap in the reticle at the bottom of the map.
The template is a <a href="//commons.wikimedia.org/w/index.php?title=Visible_Earth&amp;action=edit&amp;redlink=1" class="new" title="Visible Earth (page does not exist)">Visible Earth</a> image collected by the <a href="//commons.wikimedia.org/w/index.php?title=Earth_Observatory&amp;action=edit&amp;redlink=1" class="new" title="Earth Observatory (page does not exist)">Earth Observatory</a> experiment of the U.S. Government's <a href="//commons.wikimedia.org/wiki/NASA" title="NASA">NASA</a> space agency.  The reticle is 15 degrees in latitude and longitude.
No machine-readable author provided. <a href="//commons.wikimedia.org/wiki/User:Mdf" title="User:Mdf">Mdf</a> assumed (based on copyright claims).
No machine-readable source provided. Own work assumed (based on copyright claims).