When you think about how gyroscopes work you will realise that there are two of them in this unit: one rotating around the vertical axis to drive the attitude indicator, and one rotating around a horizontal axis to provide directional information. The fact that this information is displayed by rotating the attitude indicator display ball around its vertical axis should not be taken to imply that the designers somehow came up with a 3-axis gyroscope: that is a physical impossibility.
The DG flag indicates that the directional gyro has failed, prompting the pilot to disregard the heading indication (which can’t be made to go away due to the nature of the device).