That section is very poorly written and describes how to score FC/H when the fielder holds/checks a lead runner. It doesn't apply in this case, so you can't use it to justify scoring a hit.
Upon further review, I agree on both counts (badly worded and not applicable). Also agree if you substitute the word attempt for the word play it makes more sense.
So if you look at the entire section (8 rules) in ATEC on FC and think your way through it one section at a time, then I think the only section that possibly applies (if you take the broad definition of what is a play) is #3:
When a ball is put in play where a play is made on any lead runner and an out occurs, or an out would have occurred had no error taken place, or the runner is safe, but the batter would have been out had the initial play been made at first.
It would clearly apply if the word attempt was used in several spots instead of the word play
That means that the sitch I described above would also be FC unless in the judgement of the scorer the batter would have been safe had the initial play/attempt gone to 1B.
Thanks for educating me