At 4:44, a very very familiar sounding tune. Everyone must have heard of it somewhere. Very interesting documentary by the way.

How Music Works 1 - Melody - Part 1 - YouTube (http://www.youtube.com/watch?v=PnbOWi6f_IM)

In the episode's credits (http://www.youtube.com/watch?v=aPmnho7OvT8&t=09m08s), it says that all non-classical pieces are original compositions by Howard Goodall. That's at least a starting place.

As far as a video game music connection, the instrumentation and melody reminded me of Klonoa: Door to Phantomile.

Ya that's a pretty popular tune. Name of the song is Merry Christmas Mr Lawrance by Ryuichi Sakamoto.He is as popular as Hisaishi in japan and I recommend listening to his other songs. Here is the link to the version you heard Merry Christmas Mr.Lawrence -Original Version- - YouTube (http://www.youtube.com/watch?v=NkWjsT_SJNI)