How to enable local LAN DNS name resolution in Windows server 2008r2?

I'm running a Windows 2008r2 server in a non-Domain (workgroup) role. It is a DNS server and DHCP server for the LAN.

DNS services work fine for external Internet addresses, but local hostnames do not resolve.

c:\>ping raspberrypi1.local
Ping request could not find host raspberrypi1.local. Please check the name and try again.

c:\batch>ping raspberrypi1
Ping request could not find host raspberrypi1. Please check the name and try again.


c:\batch>ping 192.168.1.169
Pinging 192.168.1.169 with 32 bytes of data:
Reply from 192.168.1.169: bytes=32 time<1ms TTL=64
Reply from 192.168.1.169: bytes=32 time<1ms TTL=64  .....

The DHCP server lists the correct hostname for all the devices on the LAN in its list of leases, but the DNS server seems to be unaware.

How do I enable local hostname resolution?