Try playing w/o the steam overlay

EDIT: At the request of Andrea, here is my response to your comment:

The problem that your error message indicates is that Saints Row 3, a 32 bit application, is trying to load the 64 bit steam overlay. To disable the steam overlay, do both of these things to make sure: -Go into Steam (top left corner of window) > Settings > In-Game > Uncheck the "Enable the Steam Overlay while in-game" box. -Right click on saints row 3 in your library and click properties, then uncheck the same box. If it still doesn't work after this, confirm that the error message is the same as before. If not, please post it, if so, tell me and I will try to help.