My first instinct is to say no, Fey Ancestry does not grant an elf advantage on the save against this spell, because the spell does not say that it bestows the charmed condition upon its target; instead it seems to merely restrict the list of possible targets to creatures that are not immune to being charmed.
At first I was tempted to add the rules-as-written tag to this question, but I'm also curious to see if there is any significant evidence that Fey Ancestry was intended to apply to this spell but perhaps the language was simply never updated by the developers. Good answers should provide both a rules-as-written viewpoint as well as a rules-as-intended viewpoint.
This question is sufficiently distinct from Fey Ancestry - What spells and effects are covered by 'advantage against being charmed'. While the RAW answers to these two questions might be the same, the RAI answer (which I specifically asked for as well) is not considered by any of the answers to the existing question. I'm not limiting responses to a strict Yes/No RAW determination of whether or not to grant elves advantage on the save. Rather, I'm asking if there is a reasonable argument to be made whether or not to grant them advantage on the save regardless.
Relevant Player's Handbook Excerpts
Elf Racial Traits, Fey Ancestry, PHB page 23
You have advantage on saving throws against being charmed, and magic can't put you to sleep.
Spell Descriptions, Otto's Irresistible Dance, PHB page 264
Choose one creature that you can see within range. The target begins a comic dance in place: shuffling, tapping its feet, and capering for the duration. Creatures that can't be charmed are immune to this spell. A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other creatures have advantage on attack rolls against it. As an action, a dancing creature makes a Wisdom saving throw to regain control of itself. On a successful save. the spell ends.
Conditions, Charmed, PHB page 290
- A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects.
- The charmer has advantage on any ability check to interact socially with the creature.