The QuickStart downloads are intended to be run as gues OSes in Virtualbox, VMware, Docker, etc.
To use a QuickStart install, you would need the viritualization software live VMware on your Azure host.
If you just have raw Azure hosts, I assume you can either install using "yum" or "apt-get" on the hosts or use Cloudera Director to deploy a cluster.
I know you might have more questions, but I think this explains why you are having difficulty finding a "quickstart" for Azure. Azure is a cloud offering, but a QuickStart is intended to be run in a Virtual Machine, docker,etc.