The cube didn't rotate for me the way it did for you. I went to user preferences and undid the Select button, but that didn't help any. The cube seems to translate instead of rotate. I did click the arc button. I have no idea if I have an Intel GPU or not, so I don't know if this is caused by a bug in Blender or something that is missing from the tutorial.
Sorry, my description was flawed. Steps:
1. Select Object mode, select the object (Suzanne or cube)
2. Click on Transformation manipulators: rotate button. Note appearance of circular curves in red, blue, and green
3. Click/select anywhere on red or blue curve, then drag the mouse. Note that object translates instead of rotates. Note that clicking and dragging on the green curve works: the object rotates.
Looks like a bug in Blender...