  Recently, DeLaunay et al. (2016) discovered a gamma-ray transient, Swift
J0644.5-5111, associated with the fast radio burst (FRB) 131104. They also
reported follow-up broadband observations beginning two days after the FRB and
provided upper limits on a putative afterglow of this transient. In this paper,
we show that if such a transient drives a relativistic shock as in a
cosmological gamma-ray burst (GRB), these upper limits are consistent with an
environment of which density is much less than that of an interstellar medium
but typical for the outskirts' density of a galaxy when the typical values of
three microphysical parameters of the shock are taken. This appears to be
inconsistent with the catastrophic event models in which the central engine of
Swift J0644.5-5111 is surrounded by an interstellar medium, but together with
the properties of the gamma-ray transient, favors the binary neutron star
merger origin. We further constrain the physical parameters of the postmerger
object by assuming that Swift J0644.5-5111 results from internal dissipation of
a spinning-down pulsar wind, and we find that the postmerger object is an
ultra-strongly magnetized, very rapidly rotating pulsar. This merger event
should have given birth to a gravitational wave burst, an FRB, and a short GRB
or an extended X-ray/gamma-ray emission if a relativistic jet of the GRB is
missed. Such "triplets" would be testable in the near future with the advanced
LIGO and Virgo gravitational-wave observatories.
