How to sync Facebook contacts in Android Lollipop on Moto G (2nd Gen)?
Okay, I should searched a bit more before posting this question. But in my defence the answer was in second page of Google search results.

From this link I gather that:


  Facebook contacts will no longer sync with the Android Contacts app
  [on Android OS 4.1 and later].
  
  The Android Contact list is built to provide data portability, and
  Facebook provides contact data that cannot be exported from the
  device.
  
  Facebook contacts can still be accessed on the phone through the
  Facebook app.


It seems HTC had its own custom Contacts app which made the importing syncing contacts from Facebook (and other social networks) much easier. The Contacts app on Moto G (2nd gen) is stock Android and doesn't seem to have this feature.

The artilcle further suggests:


  While we cannot guarantee or warranty a third-party application, some
  owners have reported success syncing Facebook contacts using Ubersync
  and Haxsync.


NOTE: The link mentioned earlier refers to Nexus 6 but I believe it applies to other devices also and seems to be the only logical answer as of now.