I'm running Windows 7 Home x64 with Google Chrome on one machine, Windows 8 & Chrome on another. It also doesn't work in FF. I even tried IE just in case.
The fact that it is across multiple machines with different OS's and different browsers suggest it is in the application.
When I click the "call phone" button in Gmail it brings up the dialer gadget. I can type names from my contacts and it will let me pick the phone number to call. Unfortunately I've notice it doesn't recognize some contacts from my contacts Gmail contacts. I've compared a working contact and a non-working contact and haven't been able to identify any differences, poor example but like having both the first and last name in the last name field. Any ideas why the dialer sees some contacts but not others?