Isn't this a dangling something?

You're quite right. It is very awkwardly written.

I suppose it's a kind of dangling modifier (but it is 4:20 AM, so my mental faculties may not be functioning at full capacity). It certainly shares the salient feature of a dangling modifier, in that it is easily

misinterpreted as being associated with a word other than the one intended, or with no particular word at all

From the context, it is clear that the phrase “as one of the busiest times of year” is in fact supposed to be associated with the word Christmas—except there's no actual mention of Christmas. The only thing it can logically attach itself to is people, which is clearly nonsense. People are not a time of year, busy or otherwise.