It is not compulsory. Location Picker simply replaces the Location field thus removing Google dependency. And doesn't require the Locations Map module to work.

Locations Map is also a fully standalone module which just shows data on a map, it can be used with both Google or Location Picker driven Location fields. 

The Location Picker's functionality is shown on these two screenshots:
https://una.io/s/bx_market_photos/rc7jp6wswbchkd2mvmbgtf48xbquwge5.png
https://una.io/s/bx_market_photos/48nywqsehtwrme3uj2h46r6qj5q8sr9r.png