[extractors] Use new framework for existing embeds (#4307)

`Brightcove` is difficult to migrate because it's subclasses may depend
on the signature of the current functions. So it is left as-is for now

Note: Tests have not been migrated

yt_dlp/extractor/nytimes.py

@@ -103,6 +103,7 @@ class NYTimesBaseIE(InfoExtractor):
 
 class NYTimesIE(NYTimesBaseIE):
     _VALID_URL = r'https?://(?:(?:www\.)?nytimes\.com/video/(?:[^/]+/)+?|graphics8\.nytimes\.com/bcvideo/\d+(?:\.\d+)?/iframe/embed\.html\?videoId=)(?P<id>\d+)'
+    _EMBED_REGEX = [r'<iframe[^>]+src=(["\'])(?P<url>(?:https?:)?//graphics8\.nytimes\.com/bcvideo/[^/]+/iframe/embed\.html.+?)\1>']
 
     _TESTS = [{
         'url': 'http://www.nytimes.com/video/opinion/100000002847155/verbatim-what-is-a-photocopier.html?playlistId=100000001150263',