The rule says subsequent play on a different runner. You are describing the initial play on a batted ball by a batter, that is not a subsequent play on a different runner.Thinking of a slightly different version of your scenario.
Runner on second stealing, F6 obstructs. The ball is popped up, which allows the runner to get all the way to third. The ball is then caught.
Since she reached the base she would have reached without obstruction (third), does catching the pop-up count as a "subsequent play"? In this case, would the obstruction be nullified?
Also, the rule (looking at NFHS) says "an obstructed runner may not be called out between the two bases where she was obstructed." I don't like the word "between" there because it quite literally means anywhere in the space the exists from where second base ends and third base begins. "Between" doesn't cover the bases. (The numbers between 1 and 5 are 2, 3, and 4, not 1, 2, 3, 4, 5.) But I've learned from these discussions in the past that it's silly of me to expect the actual, literal definitions of words to matter when it comes to rule sets. Anyway, taken literally, in your example she could be called out since the out didn't occur between the bases. It occurred on second base.
And the rule on obstruction about "between" includes both bases.