The Logitech K600 KB does work without the online setup, but is is not a slick device and is not acceptable. The Touchpad is very insensitive and slow. There does not appear to be any way to customize it. The website to set up the final six special keys does not exist and the URL generates a 401 error. Because it is black with faint lettering, it is hard to see the keys in a darkened room which is what most TV rooms are. I expected much better from Logitech but did not get it. Mac Mini with OSX10.13 via Bluetooth.
I would expect it to be seen as a Bluetooth trackpad by your Mac mini so System Preferences > Trackpad > Point & Click > Tracking speed would customize it. Failing that, it should be seen as a Bluetooth Mouse and customizable by System Preferences > Mouse. I wouldn’t expect either preference category to support all the customizations Apple’s input devices do.
The K600 Getting Started page has information about pressing a key combination to optimize the keyboard for the particular OS it’s being used with. It also has a link to download Logitech Options, is that the software you’re looking for?
I tried the System Preferences to no effect.
Too bad they made no mention of the Getting Started page with the unit. I could have tried the download although the compatibility page does not include the K600. I spent quite a bit of time on the Logitech site and never found anything useful. I already repackaged the unit for return to Amazon.