The disallowed Tottenham goal that's shown starting from 6 mins 10 in that video came when Trautmann saved a penalty and the kicker put the rebound into the net. The award was made right on the stroke of half-time, so the ref according to the rules extended the first half to allow the penalty to be taken and blew as soon as Bert made the save.
Spurs finished third in the league that season, two points behind champions Burnley but with a better goal average. If they'd scored that penalty against us and managed to close out the win in the second half, Spurs would have been champions. I'm sure Blue Moon will be full of sympathy for them missing out so narrowly!