Notice that although the strokes are uneven, they still give a consistent look to the overall result.
A quick web search on right-brain/left-brain returns all sorts of information on the benefits of using your non-dominant hand, particularly for us right-handed folks.
We think you'll enjoy playing around with this and will probably learn a lot from doing a few Zentangles this way. At a minimum you'll have a greater appreciation of what it's like as a child learning fine motor skills, or an adult recovering from an injury.
Try it . . . even if you don't show anyone your first one! But do another. It's amazing how quickly your non-dominant hand catches on - and begins to show its own style as it energizes a different part of your brain.
Click image for larger view