Passed ball situation

[ElPanadero]

Here's the situation. Bases loaded, 2 outs. Passed 3rd strike. Runner at 3rd takes off for home, tags home before catcher gets to ball. Catcher picks up ball at backstop and throws to 1B. Throw is short, BR makes it to 1st safely. The runner that was originally at 1B is totally confused and is standing halfway between 1B and 2B. The first basemen sees this and throws to 2B for the third out.

My question is: does the run count. And, if it does, why?