1. If screenApiRotate()'s calls are the only screen function in the script, e.g.

screenApiRotate(ScreenObjectIDs.Widget_1,fAngle,x,y);
screenApiRotate(ScreenObjectIDs.Widget_2,fAngle,x,y);
processScreenApi();

The image objects will not rotate.

If an update to a text widget is added, the objects will rotate.

setTextWidgetText(ScreenObjectIDs.TextWidget_Test,"Test");
screenApiRotate(ScreenObjectIDs.Widget_1,fAngle,x,y);
screenApiRotate(ScreenObjectIDs.Widget_2,fAngle,x,y);
processScreenApi();

2. Also, the documentation indicates that processScreen() takes an argument:
processScreenApi(uint screenObjectID)
I get an error when an argument is added, e.g.
processScreenApi(ScreenObjectIDs.Widget_1)
No errors occur when no argument is specified: processScreenApi()

Sorry, not a bug. I found the fix.

Set Image Widget parameter, "Dynamic=true" to get the image to rotate when using screenApiRotate().