ok my mistake, I misunderstood and believed the marker search was not working.
Your issue maybe caused by this:
(found in the browser console on your page)
This API project is not authorized to use this API. Please ensure this API is activated in the Google Developers Console:
console.developers.google.com/apis/api/places_backend?project=_
For more information on authentication and Google Maps Javascript API services please see:
developers.google.com/maps/documentation/javascript/get-api-key
The autocomplete place search use the Google PLace API wich must be included to your API project as the Javascript Google Maps API. It seems to be missing, preventing the location search to work.
Hope it helps. Let me know.