Thanks to countless adventure stories in the vein of Indiana Jones, our view of primitivity can be a little skewed. When we think of the term, we imagine tribes of people still living in huts and throwing spears in the age of ipads and yogurt that comes in a tube. However, The Island of Dr. Moreau wants us to reconsider primitivity. It wants us to see primitivity not as a (low) level of tech-savviness but as something inside us. It's the primitive and savage remnants our ancestors left in our brains. And given the right circumstances, even the most civilized among us can give way to primitivity.
Prendick's inability to wield the weapons of civilized society—i.e. the gun and the whip—are actually signs of his civility. It is only when he uses the gun that he begins to descend into primitivity.
The whole point here is to show us that we're all primitive, no matter how much tea and how many finger sandwiches we consume. When put in the right situation, we, like Prendick, will revert back to our basic instincts... at least eventually.