There’s two main parts to Sukkos: the “Yom Tov,” on which most acts which are forbidden on the Sabbath are also forbidden (the main exception being many things that are involved in food preparation), and “Chol HaMoed,” on which some acts forbidden on Yom Tov are also forbidden, but which is generally more lenient. This year, the “Yom Tov” part of Sukkos starts at nightfall of the 13th and ends at nightfall on the 15th, with Chol HaMoed starting immediately upon the conclusion of Yom Tov and running until nightfall of the 20th, followed by a separate holiday, “Shmini Atzeres,” which is irrelevant to the discussion at hand.
As per this article (h/t Isaac Moses), the elections are open until 10 PM. Were the elections to be held on the 14th, this wouldn’t help anything; however, since they’ve been pushed off to the 15th, they are still open after Yom Tov is over and Chol HaMoed begins. As the relevant prohibitions to voting (driving to the polls and the electronics involved in the voting process itself) are permissible on Chol HaMoed but not on Yom Tov, this switch allows Jewish voters to vote the evening of the 15th.