It's a diacritic marker that indicates how the word is supposed to be pronounced, with a syllable break on the marked letters - as though readers might get confused and think the word is pronounced "reel-ection" as opposed to "re-election." It's a pretty archaic practice, but The New Yorker persists. They have a lot of unusual stylistic preferences, like preferring the spelling "vender" over "vendor," which also occurs in this article.

A more common example of the diaeresis would be the name "Zoë" - the "ë" indicates the pronunciation is "zoe-y" (2 syllables) not "zoe" (1 syllable).

https://en.wikipedia.org/wiki/Diaeresis_(diacritic)#English

Some style guides recommend the diaeresis over doubled vowels when they are pronounced separately. The idea is I believe from French: maïs, Noël, etc.

I was taught to do it that way in public school here in Canada in the 90s; it is the textbook proper way to spell words like coördination. I was also taught that no one actually spells it that way and that co-ordination and coordination are both fine and far more common.

that's the New Yorker signature style