"Dance macabre" or "macabre dance"

Most likely a typo, possibly out of (well-intentioned) ignorance. I would argue that danse macabre is a set phrase in English, similar to à la carte or cause célèbre. The ngram below suggests that the parallel English phrase dance of death is far more popular than any permutation of the translation.

"Macabre dance" would be standard grammar, but the inversion isn't wrong. Especially in poetry, and normally in foreign phrases, you will come across post-positive adjectives. In this case, the writer was probably used to the word order in the French phrase danse macabre, but spelling-wise either slipped into or attempted anglicization. I doubt it was a mistake, since there was no attempt at quotation marks or italics, and the result is grammatically fine.

That said, danse macabre even in English appears to numerically surmount the other options:

With the s, and set in italics, danse macabre is a French term that the person is using as a reference, like joie de vivre or je ne sais quoi. With a c, and no italics, macabre dance is just an English phrase like loud music or interesting painting. With mixing and matching of c/s, word order, and presence or absence of italics, it's an error of one kind or another.

In the piece from the NY Times, the writer is without doubt alluding to Saint-Saëns' Danse Macabre so to have used "Macabre Dance" would break that allusion.

How can we be so sure they were alluding to the music? For me, it seems clear that the writer is not suggesting that the performance was literally macabre, so what other intention could there be?

I think the phrase "macabre dance" would be very seldom-used. There's no allusion in it, and a dance that is actually macabre must surely be a rare thing...?