I remember even after flash player it buffered video though? They changed the behavior after Flash was dead probably as someone else suggested to not waste bandwidth on people closing the tab.
Edit: in fact every native web video player downloads as much as possible as far as I can tell.
The native <video> and <audio> tags buffer a few megabytes at a time. This is easy to see by opening a video file in the browser (not from file://) and watching the network tab.
Depends on how you set it up apparently, I assume it changed over time:
preload= "metadata" - is the default which is 2-3% of the video.
preload="none" - no video will be downloaded on page load
preload="auto" - the entire video is downloaded. (Some browsers do not do this, and only download partial videos anyway)
Edit: in fact every native web video player downloads as much as possible as far as I can tell.