Why are Merkel cells innervated by an axon, and not a dendrite?
There is nothing out of the ordinary with the Merkel cell, as it functions in the same way as photoreceptors and hair cells (see Further Reading #1).


Fig. 1. Merkel cell. Source: Gallery for Share. 

The Merkel cell depicted in Fig. 1 is a specialized receptor neuron. It has no axon. It relies on a secondary sensory neuron (a somatosensory afferent) onto which it synapses to direct the touch signal to the brain.

Note that neural information flow goes from dendrite to axon. An axon terminates into a synapse. The Merkel cell, which does not have an axon, features a synapse directly onto the dendrite of the secondary neuron (See Further Reading #2).   

Further Readings
1. Can axons act as receptors?
2. What are the functions and differences between axons and dendrites?.