When Does the Second Remake of "King Kong" (2005) Take Place?
"King Kong" is an adventure horror (kaiju) film written by Fran Walsh with Peter Jackson and Philippa Boyens [remaking "King Kong" (1933) by James Creelman with Ruth Rose, Merian C. Cooper, and Edgar Wallace] that released December 14th, 2005. So when is "King Kong" set?
It takes place in the year:
We know this because the iconic final scene is atop the Empire State Building. When Jack Driscoll runs inside the lobby, it appears to be normally open to the public. The Empire State Building was finished on April 11th, 1931 AD and opened on May 1st, 1931 AD. So it must be during or after May of 1931 AD.

1933 AD
We know this because the iconic final scene is atop the Empire State Building. When Jack Driscoll runs inside the lobby, it appears to be normally open to the public. The Empire State Building was finished on April 11th, 1931 AD and opened on May 1st, 1931 AD. So it must be during or after May of 1931 AD.
Also, a neon sign is visible in the far background of New York City for "FISK TIRES". Fisk Tires was bought by United States Rubber Company in 1940 AD and would have little need to advertise under this name further. So it is most likely before 1940 AD.
More specifically, during the Times Square sequence a large billboard is visible for the film "M" (1931), which released in the United States of America in April of 1933 AD. So it is most likely April of 1933 AD at the end of the story.
It has been retroactively absorbed into the MonsterVerse Universe at a chronologically early spot (a first chronological film to feature King Kong) and can be watched at its timeline point, as an extended flashback before "Godzilla vs. Kong" (2021) [with or without the "Monarch: Legacy of Monsters" (2023) TV show], or entirely separately.
It was adapted as a video game in late 2005.