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Some of these story games give the responsibility for certain jobs in the game to one person. That person commonly gets called the game master (GM).
Exactly what the GM does varies from game to game, but generally you can expect the GM to be responsible for providing a certain amount of structure, pacing and conflict for the other players to riff off. You might think of them as the bass player in your band.
The games that have GMs are listed here, along with a couple of notes on the GM's job in each game:
My Life with Master – the GM must play the part of the Master who orders the Minions to perform dreadful missions.
Nicotine Girls – the GM needs to throw lots of adversity at the girls, and push them to complicate their lives.
The Princes' Kingdom – the GM (called the Guide) must create the islands that the characters visit, and play the people of the islands.
Wuthering Heights – the GM throws melodramatic, conflict-ridden situations at the characters.
It's not so hard to try being the game master with most of these games, and it can be a lot of fun.