The design of the system requires the player to put their hand in the robot arm's work envelope in order to make a move, so in order to follow your advice one would have to avoid playing the game, which seems a shame.
The robot actually moves much slower than the speed in the video, so it would be hard to get caught without trying. The servos are also weak enough that they wouldn't be able to really hurt you.
Unless it's a physical limitation of the motor, "moves slowly" is still risky, because a programming error could cause the robot to move unexpectedly quickly in an unexpected direction! But "motor too weak to cause injury" is a good safety feature.
The project looks really nice in the videos, by the way — it must have taken a great deal of effort to get it working so smoothly.