Two plateaus and a following bump in the X-ray light curve of GRB 170714A have been detected by the Swift/X-ray Telescope, which could be very significant for the central engine of gamma-ray bursts (GRBs), implying that the origin of this burst might be different from those of other ultra-long GRBs. We propose that merging two neutron stars into a hyper-massive quark star (QS) and then collapsing into a black hole (BH), with a delay time around 10(4) s, could be responsible for these X-ray components. The hyper-massive QS is initially in a fluid state, being turbulent and differentially rotating, but would solidify and release its latent heat, injecting it into the GRB fireball (lasting about 103 s during the liquid-solid phase transition). A magnetic field as high as similar to 10(15) G can be created by dynamo action of the newborn liquid QS, and a magnetar-like central engine (after solidification) supplies significant energy for the second plateau. More energy could be released during a fall-back accretion after the post-merger QS collapses to a BH, and the X-ray bump forms. This post-merger QS model could be tested by future observations, with either advanced gravitational wave detectors (e.g., advanced LIGO and VIRGO) or X-ray/optical telescopes.