For those searching I am having this issue with a new 2016 MacBook Pro running sierra v10.12.1. Multiple Install->Reboot cycles with everything still plugged in but the Multiport Update is not being installed.
Your USB-C Power Cord must be plugged directly into your multiport adapter (which is plugged into your laptop) when doing the reboot. Having the adapter plugged into one port, while the power cord is plugged into another of your laptop's ports will not work.
NOTE 1: Working Layout
Wall power outlet => USB-C Power Adapter => USB-C Power Cord => Multiport Adapter => Laptop
(You don't need the external display plugged in.)
NOTE 2: When I first plugged my power cord into the multiport adapter, it displayed some weird behavior where the Driver Install prompt went away and the "charging" icon would show briefly, then disappear. I restarted my laptop with everything still plugged in and then the Driver Install prompt stayed visible.
You could probably also click the "Install" button before pluggin in the power cord and once the wizard is open, plug in the power cord. I'd guess the power cord is only required to be plugged into the multiport adapter to give the adapter power during the reboot.
NOTE 3: The time that the install/reboot actually worked, the reboot took a significantly longer time than usual. Probably about 3 mins. So if you also experience that then its a good sign.