Update: this is now fixed -
http://steamcommunity.com/games/314660/announcements/detail/234522998930417128
Hi Oddworld fans.
We're aware that a small number of users are having issues with overly responsive Xbox 360 controllers.
This is due to the deadzones on those controllers being slightly different from our testing controllers.
We're implementing a deadzone slider and hope to have news on a release date for the patch tomorrow.
Thanks for your patience.