True, I can still hit the space bar, but it does something different and broken. Try paging down on HN, and you'll see that the bottom 1-2 lines are preserved at the top of the screen, so you don't lose your place. Now try it on NYT: at least for me, there is absolutely no context preserved. That's better than the all-too-frequent case where a line is missed entirely, but it still makes reading harder. Plus, I'm so used to lousy sites that skip a line on page-down that I don't trust the NYT's version not to do so.
EDIT: They seem to do the right thing on articles, but not on the front page.
The front page is working correctly for me in Firefox 26. When I hit page down or space the two lines that were at the very bottom of the screen move to just below the top bar.
EDIT: They seem to do the right thing on articles, but not on the front page.