Q:

Why PWM pin needs intermediate MOSFET TC4420CPA to drive IRFZ44NPBF in this circuit?

Why not directly drive only with the low-pass filter? (FYI, this circuit is for constant current load)

A:

A mosfet driver is often required, but in this case it is not needed. Without the mosfet driver and with other values for the RC-filter it will also work.
The gate of a mosfet act as a capacitor. For PWM signals a mosfet driver can put enough current into the gate, so the mosfet turns on and off very fast. That reduces the heat dissipation of the mosfet.
Most mosfets are turned completely on with a voltage of about 9 V at the gate. The Arduino boards can not output that voltage. A mosfet driver can be used for higher voltages for the gate of the mosfet.
For Arduino projects, often "logic level" mosfets are used. They are already turned on at 5 V or even at 3.3 V. A resistor from the Arduino board to the gate of the mosfet should be used to limit the peak currents (because the gate acts as a capacitor).
The project of GreatScott! does not need to turn the mosfet fast on and off. The gate voltage is altered very slowly. The IRFZ44N mosfet is not a "logic level" mosfet, but the mosfet driver uses the low voltage of 5V, the same power voltage as the Arduino Nano.
The mosfet driver can be removed. The 10 Ω of the RC-filter is too low for the Arduino Nano, but a RC-filter with 470 Ω and 10 µF will do the same in my opinion. To protect the Arduino board, the 10 A fuse has to move to the high side (at VCC).
Because of the high currents of this project, the mosfet might blow. The mosfet driver provides extra protection in case that happens. The fuse is slow.
The "DIY Adjustable Constant Load (Current & Power)" project of GreatScott! at instructables: www.instructables.com/id/DIY-Adjustable-Constant-Load-Current-Power/
His explanation in the video about the mosfet driver: youtu.be/VwCHtwskzLA?t=334

