It is following the 1986 Watchmen comics, not the 2009 movie adaption.
As the word-of-god answer was already given, here is how you can figure this out on your own by just watching the series.
The most glaring difference between the comics and the movie adaption, as pointed out in the question, is the nature of the attack on New York city.
In the comic book, Adrian makes it look like aliens attacked earth by materializing a giant squid in the middle of the city. In the movies, he blames the attack on Doctor Manhattan, basically just blowing up the city and leaving behind some particle traces that look suspiciously Doctor Manhattan-y.
This is relevant as in the very first episode of the HBO series we see
a weather phenomenon in which hundreds of tiny squids rain down on the city of Tulsa, disintegrating just moments after they hit the ground. It is later explained that these kinds of weather phenomena occur on a global scale as an aftermath to the initial "alien attack".
It should be noted that, much in the same fashion as Alan Moore used to radically modernize and often completely change the tone of the comic book series he adapted in the 1980s, HBO's Watchmen takes great liberties with the source material and focuses heavily on themes that are not part of either of the previous adaptions.