VIDEO GAME ORIGINS
In the video game, thieves often steal supplies from your party. Thieves are a major obstacle in completing the journey to Oregon, and can often be responsible for the death of some or all of the party.
In the video game, there can occasionally be fires in the wagon which destroys supplies. While it is not stated in the game that a thief set the fire, this is the basis for Mcdoon being an arsonist in the musical.
In the musical, Mcdoon is a thief who frequently steals supplies from travelers on the Oregon Trail. He travels with a sidekick named Cletus Jones, with whom Mcdoon occasionally has sex with. Mcdoon sees the Daughter and desires to make her his "child bride", but the Mother refuses.
Later, Mcdoon and Cletus sneak up on the family, set fire to their wagon, and kidnap the Daughter. Mcdoon again tries to marry her, but she refuses. Cletus, meanwhile, is actually in love with Mcdoon and it jealous of the Daughter.
Mcdoon plans to bring the daughter to Mexico by caulking the wagon and floating down the Columbia River. However, the wagon hits a rock and everyone falls off into the river. (This is a reference to the video game where hitting a rock in the river will lead to the death of one or more party membes and the loss of supplies.) He and Cletus attempt to cling to a rock, but he accidentally makes his "Bandit King" gesture with his hand and lets go of the rock, killing him and Cletus.