As far as we know, any part of the trackpad can be divided and designated as a separate button. Kind of like how Apple's touch mouse (or laptops with a combined trackpad and button) can detect a right click, but with much higher fidelity than simply detecting right or left.
Presumably the configuration for a dual FPS will have the right trackpad perform absolute position tracking (for mouse look) or thumbstick emulation (for games that don't properly implement proper mouse look) in the center and middle portions of the trackpad. The outside ring can be configured for button presses and appears to be marked off by a ridge to give some some tactile feedback as to where it is located. The very center of the trackpad is also marked off with a ridge, likely to indicate where the dead/neutral zone is when the trackpad is being used like a thumbstick.
The outside ring can presumably divided into 4 quadrants for 4 buttons or even possibly into 8 and 16 segments for more buttons, but I am going to guess that 16 segments would cause problems with fat fingering buttons because of the lack of ridges to separate the buttons (It actually might be a good idea to have the outside ring divided with ridges to separate it into a number of segments that can be felt. Another solution may be to put a rigid ring over the the trackpad to but a hard boundary between the center of the trackpad and the outer ring. The ring would be suspended over the trackpad by spokes, for lack of a better term, that would also server to divide the ring into segments). The haptic feedback could come into play when the outer ring is touched, but not pressed, to resolve some of the issues with the lack of bumps...
In a standard thumbstick design, having buttons surround the thumbstick is poor ergonomically, because the thumbsticks surface is usually raised far above the surface of the buttons. In such a controller making button presses would be awkward as the thumb stick will simply interfere with button presses. The Steam controller, however, proposes a controller where the thumb controls are at the same elevation as the possible virtual buttons, which allows them to be accessed without interference.
I am skeptical of how well the haptics can give feedback where people are used to having thumbsticks that resist you pushing them out of the neutral position. I however feel that the potential control schemes offered by the trackpads are not a limiting factor. They seem pretty versatile and capable of handling many different configurations.