Reddit has a group for recorded videos showing the stories to various video games.
Non-Apple Computer Games
Mr.TVCow's YouTube channel has a bunch of funny videos related video games, entertainment, visual/special effects, etc.
Idoiocracy's Reddit re(ply/sponse) mentioned his The Making of Games' alphabetical index of all submissions with many links including videos.
MarphitimusBlackimus/Marphy Black/Revenant100's YouTube channel has a playlist, with currently 24 videos and 2.5 hours, showing "Half-Life Fact Files -- Do you want to learn more about Half-Life? To see the obscure? To witness the oddities? Then, you've come to the right playlist!
Blue's News shared The Verge's article on "How Atari box art turned 8-bit games into virtual wonderlands -- Modern games have nothing on these cartridges... The original Atari featured a wealth of games with box art that was quite a bit more imaginative than the “grizzled man holding a gun” template that’s so popular today. The concept of playing a video game in your house, on your television, was still in its infancy in the late 1970s, and Atari needed a way to market its games. One solution was to commission intricately detailed covers that sold the idea of a game much better than any simple screenshot could..."
This GamerSpawn small YouTube playlist "takes you on a trip through the history of some of the world's best game series."