Energy Source for Gamma Rays from Merging Neutron Stars
Not Nuclear fusion;
There is also a huge amount of nuclear fusion that creates heavy elements from all the iron there is in neutron star: they in fact are not only made of neutrons. But as said in comment, building of heavier elements rather consumes energy than it generates some.

Not sure scientists  has a clear agreement on how this works. 

Gravitational collapse

For example I found this (rather old) abstract which states it could be a result of gravitational collapse, without singularity (since here the result of the merger might not be a black-hole, or the lightest ever: around 2.7 solar masses!)


  theoretical developments (string theory, quantum gravity, critical collapse), which suggest that complete gravitational collapse can occur without singularities or event horizons 


Thermonuclear event again: fission

From Space.com, they say Kilonova energy could be explained by rapid atomic decay of heavy elements


  The mergers of dense cosmic bodies that are thought to cause short gamma-ray bursts can also blast out neutron-rich gas that rapidly generates heavy elements such as gold and platinum, scientists say. These "r-process" elements can undergo radioactive decay and release an enormous amount of energy — 1,000 times or so that given off by stellar explosions such as novas. These powerful events are thus known as "kilonovas"