It is an ancient custom, from the time of the Holy Temple, for a bride to ascend the Temple Mount for prayer and spiritual preparation before her wedding.
It is the custom for all people who enter the Mount to advance toward their right as they proceed around the Mount. However, it is also the custom, again, from the time of the first Holy Temple, built by King Solomon, that all those who find themselves in unusual personal circumstances make their way around the Mount advancing toward their left. This includes both individuals in mourning as well as people celebrating personal accomplishments. Included in this latter category are brides, (and grooms), on their wedding day.
According to Mishnah Midot 2:2, when one sees an individual or group of people advancing toward their left, they are to approach them, asking, “Why are you advancing toward your left?” If the person answers that they are in mourning, the consoling reply is, “May He who dwells in this house comfort you.” On the happy occasion of witnessing a bride on the Temple Mount, the reply is, “May He who dwells in this house bless you and your betrothed with love and joy,” and naturally, “Mazal tov!”
In this video we witness just this, as first we hear the maker of the video inquire of and then bless the bride, and a moment later, Rabbi Richman doing the same. Following this, a kohen present among the group is asked to describe how the kohanim would bless the people in the Holy Temple. This enabled the kohen, (who, along with every Jew on the Temple Mount, is under the constant scrutiny of the police and the Muslim Wakf), to utter the priestly blessing in spite of the draconian unwritten edict enforced by the police forbidding any form of Jewish worship on the Temple Mount.