Mac OS X itself has no built-in support for touch-screen monitors, therefore if you do want to use a touch-screen monitor capability in OS X you need to install a driver to support this.
I don't believe HP provide such drivers as standard themselves but you would need to check with them. As lllaasssuggested it is possible to get third-party drivers for various touch-screens typically you have to pay for the drivers.
Note: The driver might be listed under a name other than HP as many makers use touch-screen technology from another company and the driver would support all makes using the same underlying technology.
Yes, the touch-screen monitor should work in Windows 8 (or 8.1) running on the Mac mini via Boot Camp. The monitor is connected to the Mac mini by both a USB cable - which passes the touch-screen signals, and a DVI or other video connection. Windows 8 should then be able to talk to the monitor via the USB cable.