I encountered the same problem under Windows 10 using PD13 with AMD Catalyst 15.7.1 , the Hardware Encoding option was greyed out. My graphics card is an MSI AMD R9 280.

I managed to resolve the issue by installing the "AMD Catalyst 14.12 WHQL Omega" drivers from

http://www.guru3d.com/files-details/amd-catalyst-14-12-whql-omega-download.html

and now the Hardware encoding is available. I downloaded the 64bit driver for Windows 8.1 and seems ok under windows 10, but there will be no DX12 support.

BUT first uninstall the existing drivers using the AMD Catalyst Install Manager and clean the registry using the "ccleaner" tool from

https://www.piriform.com/ccleaner.

Reboot when instructed before re-installing the drivers.

I did try the AMD Catalyst™ 15.9.1 Beta drivers, but they made no difference with PD13, but the encoding was available with a trial version of PD14.