Here's how it works: The software has several choices for actions you can take. So, taking the disappearing cube as an example, once you're hooked up to the headset, you're directed to run a short, six-second test, where you concentrate on doing something, anything, with your mind--relax, focus, whatever.
Then, once you've completed the test, it's you against the cube. And the challenge is to see if you can reproduce what it was you were doing with your mind during the test; If so, the cube slowly disappears.
In my case, it disappeared, then came back, then disappeared again and then came back. Repeat.
They also ran me through another example, this time trying to pull the cube forward. This one was harder because the brain function I chose to do to synchronize with the challenge was more concentrated. It involved me sort of tensing up my head and imagining the act of pulling the cube forward. It didn't work very well.
But with the disappearing act, I simply relaxed my mind, with much better results.
Of course, there's no relationship at all between brain activity that is consciously trying to "pull" the cube forward and what happens. That is to say, it doesn't matter in any way what you're doing with your mind, so long as what you do during the six-second calibration matches what you do when you try to enact the action.
So really, the software is just looking for a pattern match. It's not all that complicated a concept, though I'm sure it's a pretty difficult engineering feat.