How can I make Logitech a 4K PRO MAGNETIC WEBCAM work with a mid-2011 Mac mini?

Thanks to Steve Chambers and bmike. Logitech did respond after a little while, and advised that I return the webcam. I returned it to the Apple shop, which reimbursed me.

This web cam will not work on the Mid-2011 Mac mini because it does not meet the system requirements.

Per the Technical Specifications, the Logitech 4K Pro Magnetic Webcam (for the XDR Display) requires a USB 3.1 Type C connection.

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Per the Technical Specifications of the Mac mini, it only has USB 2.0 ports.

Bottom Line

This webcam will work with any computer that supports a (minimum) USB 3.1 connection with a Type-C connector. Note, it's not Thunderbolt, however a Thunderbolt 3 port will carry the USB 3.1 signal. Thunderbolt 1 or 2 do not have support for USB.

It will also work with any computer with USB 3.1 including PCs. Additionally, it will work with other displays as well, but it was designed for the XDR display. Per the FAQ:

The webcam will work with other displays, however, you won’t be able to use the magnetic mount. It has been specifically designed for the Pro Display XDR. Additionally, the included cable’s length and connector angles have been optimized for this specific display.