The MAX5920 requires a capacitor between GATE and SENSE pins but the MAX5921 removes this condition. Do I need to install a capacitor between GATE and SENSE?

The MAX5921 implements a gate-source clamp internal to the IC that prevents the gate voltage from exceeding about 16V relative to VEE. This clamp circuit also helps to prevent the external FET from accidentally turning on during hot-insertion since it acts like a large capacitor between the gate and source. 

Adding an external gate-source capacitor can damage an internal bipolar transistor that connects its base with the SENSE pin, emitter at VEE and collector to GATE. The transistor is used as a strong pull-down to protect the external FET in case of a strong short. 

If you consider a strong short of the drain of the external FET to the positive rail, there can be a huge spike of current flowing instantaneously and producing a drop across the external sense resistor even higher than 700mV, enabling the above mentioned bipolar transistor and also the active clamp. With an external 4.7uF  capacitor between gate and source of the external FET, and no series resistor to limit the current, the internal bipolar transistor might  get damaged considering a total charge of Q=C*V = 4.7e-6 *18= 85uC, assuming Vgate=18V. The internal bipolar transistor could not withstand the high power dissipation requested to completely discharge the capacitor. The external FET could also get damaged because the pull-down could not be efficient to immediately turn it off.

It is recommended not to connect an external gate-source capacitor to the MAX5921.