Understanding Pole-zero plot
You got your stability criteria wrong: left/right plane criteria are for analog systems, i.e. when the transfer function is a Laplace transform (s-domain).

When you're dealing with discrete-time systems, and hence you're using the Z-transform, the system is stable if all the poles are strictly inside the unit circle. Therefore your system is stable.

EDIT (Due to more accurate scrutiny)

From the drawing you posted, it's not clear whether its Region of Convergence (ROC) is the shaded area outside the smaller circle, or its inner (unshaded) area. In the former case (ROC is the shaded area) the unit circle is well inside the ROC, therefore the system is stable and causal. On the other hand, if the ROC is the smaller circle's interior, then the system would be anti-causal and unstable.

Please note that the knowledge of just the transfer function (or, worse still, just its poles, as in this case) is insufficient to determine whether the system is causal or not. You need to know its ROC as well.

To recap:


Stability is achieved if the unit circle is inside the ROC.
Causality is achieved if the ROC reaches infinity.