The ump called the third strike, then pointed toward first -- Piersynski saw this and immediately spun around and headed to first. The ump then made the call again to make sure everyone saw it.
The catcher made a cardinal sin I always tell my kids during football and baseball practices -- ALWAYS ALWAYS ALWAYS play the play through completely. You keep playing until the Ref has blown the whistle or the ump had yelled OUT, SAFE or TIME!!! In this case the Catcher immediately tossed the ball away BEFORE the umpire finished calling the entire play. The replay clearly shows the catcher up and heading off before the ump ever points to first base.
The call was a bad call in my opinion. But in defense of the ump and others, the ball clearly bounces before settling in the webbing of the mitt. As there is no telltale puff of dirt, it looks like the catcher got the mitt underneath the ball.
The umpire called strike three, but as I'm sure you're aware, whether or not Pierzynski had reached safely, the play would still go in the books as a strikeout. The umpire has to account for every pitch, just as the official scorer has to account for every base gained by a batter-runner.
The umpire signaled strike three because Pierzynski swung at the ball. He had no option. But there were eight Angels facing the play who could and should have seen the umpire point to first base, and a catcher who should have realized that in a 1-1 game in an ALCS, you make sure of the out by tagging the batter anyway. That's common practice.
In short, you're right. It is not cheating to run out a play.
Another way to say that is catching the ball.
Still, a guy cannot run out of the baseline.