Rav Yosef uses this teshuva to highlight the difference between Taanit Esther and the other fast days. Whereas the other fast days are sad days in commemoration of various stages of the destruction of the Beit HaMikdash, Taanit Esther is merely a memorial to the fasting of the Jews that led to their ultimate victory in the Purim story. Rav Yosef goes so far as to label it a taanit shel simcha.
That being the case, does a groom during his week of sheva brachot fast on Taanit Esther? Even though he would have to fast on any of the other fast days in such a situation, for the reason that his personal simcha does not override the communal mourning, since Taanit Esther is a not mourning, and has some aspect of rejoicing, his personal simcha can override it.
Rav Yosef concludes by noting that the same law applies to the participants in a Brit Mila (father, mohel, sandek), and that none of these individuals are allowed to be strict and fast anyway, since it is a personal holiday for them and they have to rejoice through eating.