The following rules are relevant here:
How a Run Scores, Rule 5.08:
5.08 How a Team Scores
(a) One run shall be scored each time a runner legally advances to and touches first, second, third and home base before three men are put out to end the inning.
EXCEPTION: A run is not scored if the runner ad- vances to home base during a play in which the third out is made (1) by the batter-runner before he touches first base; (2) by any runner being forced out; or (3) by a pre- ceding runner who is declared out because he failed to touch one of the bases.
Rule 5.09(b)(6), which defines "forced out":
He or the next base is tagged before he touches the next base, after he has been forced to advance by reason of the batter becoming a runner. However, if a following run- ner is put out on a force play, the force is removed and the runner must be tagged to be put out. The force is re- moved as soon as the runner touches the base to which he is forced to advance, and if he overslides or overruns the base, the runner must be tagged to be put out. However, if the forced runner, after touching the next base, retreats for any reason towards the base he had last occupied, the force play is reinstated, and he can again be put out if the defense tags the base to which he is forced;
In the example given, the run scored before three were out, and the third out was not scored on a force play. As such, the run counts.
I assume the question here is, "is failing to tag up a force play"; the answer is no. While the runner is put out in a similar manner (by tagging the bag), it is not considered a force play.