warming up

[southump]

Bases loaded, two outs. Batter grounds to third. thirdbaseman elects to tag runner from second. slowly walks to tag him standing close to second base. Runner from first pass him on his way to third, meanwhile runner from third has scored. Does run counts?. I think it does because it wasn´t a force out but a rule´s passing a preceding runner.
would you guys let me know your oppinions and why´s