Count the run if INT

[Cecil4]

I am a softball umpire, which might be why I have this question about baseball.

One out, bases loaded, ground ball to shortstop. F6 steps on second for out #2;
then attempts to throw to first. The runner from first interferes with the throw and the INT is called.
Umpires convened.

Is baseball the same as softball, meaning the runner closest to home would be out?

In this case, in softball the runner from second to third would be out #3,
because the runner from third crossed the plate before the INT.
Why would the run not count?