I believe the system requirements for the Governance Dashboard on Qlik Market are a bit outdated, I see no reason why it shouldn't run on Windows Server 2012 R2.
But probably mto could confirm this officially.
Yes, you can run it on Server 2012.
I would, however, recommend you use the Governance Dashboard 2.0 (in Beta at present) because that does not require installation and is a standalone .qvw - meaning it should function in any environment supported by QlikView desktop and server.
Find the 2.0 version here: QlikView Governance Dashboard 2.0 App Beta (Retired)