Or maybe the other way around. I've noticed that when performing an activity that requires your unconscious/autonomic part of your brain to take over, memory recall will actively interfere with your ability to carry out that activity. We usually think of it as confidence or the ability to overcome distraction but I think it really comes down to clearing your mind of conscious thought/memories and allowing your other brain to take over.
Think about what it felt like to learn to type. At first, you had to think about which finger to put where to get the letter you wanted. But at some point, you had to start taking little leaps of faith and stop thinking about it. The same goes for sight reading on the piano. You don't have time to stop and think about what the notes mean and where you have to move your fingers. You have to just /do/ it. And if you start getting plagued with conscious thoughts and memories while you're in a performance, it will cause a distraction and lead to a memory slip, totally derailing the performance. The same goes for carrying a cup of hot coffee up the stairs. If you concentrate on the task of which foot to put on which step and making sure the cup doesn't tilt, you're sure to trip or spill it.
So I don't think it should be any surprise that performing a tetris-like activity supresses memory. Or rather, it requires the suppression of memory to do it well (or at least try to do it well).