Have you checked that the setting for the 'vibrate' feature is not set to off?
Here is a link to the Ifixit guide on how to teardown your Nexus 6.
Unfortunately, the vibration motor is mounted on the motherboard, so if it is defective you will need pcb component removal/replacement expertise and tools.
Also a preliminary search on the web doesn't show any sources for a replacement part, so unless it is loose on the board you may have to be patient in finding a spare. If you can get another Nexus 6 on Ebay, advertised as faulty good for parts, in your case one with a cracked screen, water damaged etc would be ideal as long as the price was right.
Nexus 6 Repair