It's both. Buffering the whole video was a waste of bandwidth and the changes for HTML5 means they could get away with lowering the buffering limit without destroying everyone's viewing experience.
For longer videos, a lot of people will stop watching before the video ends. A lot of bandwidth is wasted by buffering the entire video when the user is only going to watch 50% of it. To save bandwidth, sites like YouTube only buffer a tiny bit at a time.
I meant something like opening a two hour long podcast and only listening to 30-60 minutes before closing the tab or switching to a different video. With the old functionality and current internet speeds, it likely would have buffered the entire video in only a few minutes. It could have wasted multiple GB of bandwidth.
What he means is that, in olden days, videos would just keep buffering until the whole video was loaded. Now it's only at most the next ~1min, no more. You were able to see the grey bar thingie go all the way to the end.