How does an electrical impulse spread in a muscle fiber spread from the motor end plate?
Skeletal muscle cells are excitable, like neurons. Enough summation of end-plate potentials causes the cell to reach threshold and fire an action potential (which then spreads throughout the cell membrane through positive feedback, just like a neuronal action potential).

There are some differences between skeletal muscle and typical neurons, like greater importance of chloride in setting resting potential in muscles, but otherwise their action potentials are driven by voltage-gated sodium channels, just like typical neurons.

You quote:


  the amplitude of EPP declines progressively with increasing distance from the end plate region.


which is true as long as the threshold potential isn't reached, and would also be true for subthreshold receptor potentials or post-synaptic potentials in neurons. 

In the reference you link to, I assume you are referring to the mention of curare. Curare blocks the nicotinic acetylcholine receptor, so it is interfering with the end-plate potentials themselves, rather than the intrinsic excitability of the muscle.



See: 

Philip M Hopkins, Skeletal muscle physiology, Continuing Education in Anaesthesia Critical Care &amp; Pain, Volume 6, Issue 1, February 2006, Pages 1–6, https://doi.org/10.1093/bjaceaccp/mki062