How do you install the VirtIO HDD drivers for KVM on Windows 7?

You have to use the correct drivers for your OS or, as you've discovered, it won't work. The driver ISO that you're using is old. The current drivers are located at https://fedoraproject.org/wiki/Windows_Virtio_Drivers. They're signed by Red Hat so that they'll install on Windows without complaint.

You'll need the viostor driver.