Does the anatomy of our hand result in (computer) mouse-accuracy that varies by direction of movement?
Assuming the case where you move a mouse left and right with the wrist and up and down with the fingers, then yes, finger movements are more precise. The fingers and facial musculature are body parts with the most exquisite fine motor-control. The wrist, on the other hand, probably less so. The wrist is definitely involved in fine motor skills such as writing, but the fingers even more so. 

I wasn't able to find a good reference about the level of precision for different body parts at the behavioral level. I can, however, approach the question from a neurophysiological point of view. The amount of motor control available for different body parts can be visualized by means of a motor homunculus. The motor homunculus shows how many neurons are available in the cortex for a given body part. The larger the cortical surface dedicated to a body part, the larger the corresponding body part is presented in the homunculus (Fig. 1).

 
Fig. 1. Homunculus drawn on the motor cortex (left) and the homunculus presented as a figurine (right). Sources: Conference on Human factors (1997) and Autism Index, respectively. 

The fingers have a huge amount of motor cortex dedicated to them compared to the wrist. There are a lot of 'buts' to add, most notably the larger number of muscles in the fingers versus the wrist, which explains part of the difference. Nonetheless, the homunculus does show the relative functional importance of the fingers in motor processing power of the brain, while the wrist is virtually invisible on the homunculus (Fig. 1, left panel).  

Lastly, you seem to be mixing up 'distance' and 'precision' in your question. While the wrist may cover a greater distance, it is not because of this that the precision is smaller. The fingers have more neuronal processing power behind them and can be exquisitely fine tuned. In other words, the precision is not determined by the dynamic range (distance), but by the processing power dedicated to the motor function.  

As a side note, because of RSI, it is recommendable to use gross arm movements instead of fine wrist and finger movements.