Alpha-Beta Pruning with simultaneous moves?
The thing is that with simultaneous moves, the optimal strategy is harder to guess, because you need to compute something that is not always obviously winning.

Have a look at Nash equilibrium and the prisoner's dilemma if you don't know them yet. This is the kind of reasoning that you will need each time you are considering two simultaneous moves, instead of simply choosing a move that goes into a winning configuration in games with non-simultaneous moves. The concept of dominance replaces the concept of winning.

The algorithm in your reference does that when referring to figures 4 and 5 but first try to figure out what those figures are supposed to do before understanding how they do it.