I like the idea, but the first thought that came to mind (and that you also mentioned) was "Man, pieces are going to fly in all directions". If a player moves the platform a bit too forcibly towards him/herself, when s/he stops it the pieces will keep moving in the same direction, and just spread all over the place. Even if they don't actually leave the board, just moving around on top of it can wreck games with a lot of moving pieces. You want a platform with a lot of "inertia", as in, something that can't accelerate or decelerate too quickly.
Something else, it looked like the platform was trying to get to a given position during the last few seconds. I don't know if your platform was unbalanced, or only the table, but you probably want something that can stay stable while oriented in any direction.