Brookji

Does the run count? Bases loaded, 2 outs. Batter hits a ground ball to 3rd base. The runner on 2nd going to 3rd stops halfway to 3rd and waits to be tagged by the 3rd baseman. Before the tag is made, the runner previously on 3rd touches home. Does the run count? The way I read the rule is the run would not count if the 3rd baseman touches 3rd base because that’s a force out but what happens now that the 3rd baseman tags the runner. He didn’t take the force out, he tagged him which is different than a force out. Had this been the hitter running to 1st and he got tagged out I could see the run not counting, but it being another runner I think the run should count because the fielder did not take the force.