The writer “saw no issue whatsoever with men and women standing in place moving to the music”
Apparently, the writer is unaware of many sources that prohibit mingling of the genders:
It is forbidden for women to mingle among the men, either at a ritual meal or at any other occasion; rather must women be apart and men apart, for we reason from the lesser to the greater: if for a time of mourning it is written that the House of Israel shall lament every family apart, the House of David apart and their wives apart, how much more is separation necessary at feasting and rejoicing, for then the Evil Impulse is provocative (Sefer ha-Pardes, 19b).
Do not mingle sons amid daughters, lest they sin. [We read:] Then shall the virgin
rejoice in the dance alone; but the young men and the old together (Jeremiah 31:13). So also, boys and girls playing in its broad places (Zechariah 8:5)- boys apart and girls apart.
And again toward the end of Psalms (148:12), Young men and also maidens,’ it does not read, “Young men with maidens,” like [the continuation], old men with children (ibid.).
[The extra word] also signifies that, in addition, women should also be separate (Sefer Chasidim, ed. Mekitze Nirdamim, 60).
The Mishnah in Sukkah (51a), which records the proceedings of the simchas beis ha-sho’eva in the Beis HaMikdash: “One who has not seen the happiness of the simchas beis ha-sho’eva (water drawing) has not seen happiness in his days. After the first Yom Tov of the holiday, they went down to the ezras nashim (women’s courtyard) and would make a great modification (tikkun gadol).”
The Gemara (51b) explains the nature of the tikkun gadol “What was this great modification? […] The Rabbis learned: Originally, the women were inside and the men were outside, and they would come to lightheadedness. They established that women should sit outside and men inside, and they still came to lightheadedness. They therefore established that women should sit above and men below.”
They [the Sages] came across a verse and interpreted it: And the land shall mourn, every family apart: the family of the house of David apart, and their wives apart (Zechariah 12:12). Said they: Can we not reason from the lesser to the greater? If in the [Messianic] future when they will be occupied with mourning, and the Evil Inclination will have no sway over them, the Torah says that men and women shall be separate, now that people are engaged in festivity, and they are subject to the Evil Inclination, how much more certainly must they be separate (Sukkah 52a).
In his commentary to the Mishnah in Sukkah, the Rambam states that the purpose of the separation is that the men should not look at the women. However, in the laws of Lulav (8:12) the Rambam suggests a different reason: “so that they should not be mixed with one another.”
Thus any mingling of the genders at an organized public event is prohibited.
Rav Moshe Feinstein writes that for gatherings that are non-obligatory, such as weddings, he is in doubt as to the need for a mechitzah. He proceeds to bring a number of proofs that there is no obligation to erect a mechitzah for non-obligatory events, as we find concerning eating the Korban Pesach, and in other sources.
However, in another teshuva (Yoreh De’ah Vol. 4) he notes that the obligation for a mechitzah applies to all events that are open to the public, and not to private affairs (such as weddings) that are not open to the general public.
For a Torah lecture open to the general public Rav Moshe writes (Orach Chaim 5:11) that there is an obligation of a mechitzah (since it is open to the general public), but if there is no option one should not refrain from teaching in such an environment, where doing so is for Kiruv purposes.