Many video players were still using flash. VKontakte still had its flash app/game platform going strong, though you did have the option of using an iframe that loaded a web app from your server instead. Flash support was only discontinued there around several years ago.
I personally remember being rather annoyed when our uni project in 2012 had to be built with Flash and AS3 as it was well known that flash would get the axe in a few years.
We had the option to use JS as well but it wasn't in the curriculum and 4 out my 5 person team didn't want to do any of the extra work.
Even if Flash was used, it was mostly video players and some online games (like Newgrounds). I think YouTube came out with their HTML5 player in 2012 so Flash was definitely moving into a more niche status and I don't consider it essential after Flash based sites went out of fashion (which was closer to 2008-2009. HTML5, ECMA5 and CSS3 (or just HTML, JS and CSS as it's known today) largely made flash redundant before 2012.
There;s a difference between still being around and being an "essential part" of the web.
Flash was almost certainly not an essential part of the web. 2012 was 5 years after the iPhone and by then Android and iPhone constituted the majority of web browsing, and neither supported flash at all.
You couldn't very well say something was an essential part of the web if it wasnt supported on those devices in 2012.
