You can avoid the exception just by setting the style.CellvalueType to int.
this.gridDataBoundGrid1.Binder.InternalColumns["enumtype"].StyleInfo.CellValueType = typeof(int);
But this will just display the int value in the grid column as opposed to the name of the enum value.
If you want to see the name of the enum value in the column, then you will have to derive the cellmodel, and override the GetFormattedText method, casting the value to the enum there. Here is your sample back with some minimal code.
WindowsApplication1_6569.zip