How do I make Microsoft Arc Touch Mouse middle-click on single touch?

It is probably too late to answer five years after asking... There is an option now that is documented and supported by MS to simulate a standard middle click with one tap using Three Finger Click. Not sure it was an option that times. Also not sure it is much more comfortable to perform a single tap with three finger rather than double tap anything. But hope it helps those who stumble upon this answer. It just works and supported.

All you need for this is two following steps (no reboot):

• Download and install Mouse and Keyboard Center of MS
• Set Three Finger Click to Middle-click (as it is disabled by default)

I've found the answer here in the forum post of 2018 in MS Community.

This is how this setting looks like: