the pit lane and starting point is correct where it is currently between Club and Abbey. it is true that the pitlane between Woodcote and Copse still exists since it is used in the National layout for GT Cars, Touring Cars etc. and the Club-Abbey pit lane is used in the Grand Prix layout for Formula racing. nothing wrong here.
in response to the video, it is a bit outdated and Red Bull probably hadn't updated their simulator at the time of recording. the video was uploaded in mid 2010 and the track layout has only been in use since 2011. it seems like they didn't know of the pitlane/finish line change back then.
edit: added a picture showing the different layouts
here