Is there any way to turn off the animation Screen Cleaner Pro does? It seems to come on every 10 minutes or so. It's really, really bad when I'm playing games.

Screen Cleaner Pro was an April Fools' joke, and is completely useless.

As TAC said, Screen Cleaner is simply a joke. Ambrosia pulls something like this every year, and there have been several topics about it's un- or reality.

So just quit it and you'll be fine.

Did anyone else start laughing uncontrollably as soon as they read this?

Not quite uncontrollably, but it was worth a good chuckle.