Can one talk about deacetylation of a promoter rather than associated histone?
The authors obviously meant to write that the histones associated with the promoter become deacetylated. They cannot mean the promoter itself as that is DNA.

What they wrote is not shorthand or acceptable alternative usage, but just a mistake — published papers often contain typos and mistakes of this sort. Probably the authors meant to write the technically correct form of words but lost a phrase. Or perhaps they had exceeded the limit to the number of words allowed in the summary, and so they went through trimming, but trimmed too much.

Why didn’t the referees pick this up? Of course they should have, but they were probably more concerned with the contents of the paper and whether the experiments described by the authors justified their conclusions. They are busy scientists and probably doing the job voluntarily.

In conclusion, scientists are human, scientific writing is difficult, and everyone makes mistakes. But we should still try to convey our ideas as clearly as possible, and certainly not copy something that is technically incorrect or ambiguous, just because it has made it into print.