I'm going to cheat by referencing the patent. ;)
Automatic Bar Controls owns the Wunderbar site and has a patent on the product. The patent is US008925769. The actual detail drawings don't seem to be available there though, so you have to get it straight from the US Patent Office listing.
The name of the patent is: Wireless spout and system for dispensing.
Embodiments of the present invention provide a pouring device for a container for the dosing of liquid. The pouring device has various features intended to ease use, including an improved removal and attachment system and a system to identify and visually illustrate selected pour sizes. In a specific embodiment, the pouring device has a colored light or LED indicator system that allows the user to quickly and easily confirm the selected pour size. Embodiments may also include one or more features that ease attachment and removal of the pouring device to a liquid container, such as a replaceable cork system.
The specific part is Claim 1:
(c) an electrically operated valve disposed within the spout housing for selectively clamping the conduit so that a registerable amount of liquid is dosed;
That seems to answer the question of how it works. It physically clamps off a tube to stop the flow of fluid. More specifically from the description in the patent:
The silicone tube can be easily squeezed to stop the liquid flow. This can be done by a stepping motor, a motor with gearbox, or any other motor or appropriate mechanism.