Incorrect Button Mapping when using Wireless Xbox 360 Controller

When I plug in the dongle and load up a game such as Goat Simulator or Stranger Oddworld, the triggers are mapped to the right analogue stick. This means my view constantly rotates and moves upward. This is because the inputs are registering -1.0. When I move the triggers toward the centre of movement, the view stabilises.

Can the triggers be remapped?