The New York Times is hurting financially these days, and its online business doesn’t seem to be helping much, but at least it keeps pushing forward. One area where the NYTimes.com has put a lot of effort is in video, and it has just redesigned its video page around the new Brightcove 3 player. Previously, the NYTimes was using the FeedRoom as its main video platform. (This swap doesn’t come out of the blue. The New York Times is an investor in Brightcove).