The datasheet for the IRF1404Z does indeed show that the TO-220 package variant has a limit of 120 A continuous at 25 C. It should be noted that the junction temperature is rated for up to 175 C, which might provide a lot of headroom for, but we'll see.
The minimum dimensions for the drain and source leads are 0.36 mm by 1.14 mm. This gives us some 0.41 mm^2 cross sectional area. Assuming the leads are made of aluminum -- I'm on mobile and can't quickly check the composition for the generic TO-220 package -- which has a resistance of about 60 Ohm per km, and with the lead being a maximum length of 14.73 mm, the resistance of either lead will be some 0.88 mOhm.
At 120 Amps, the resistance heating would be about 12.6 Watts. That's quite hot for a short lead, and there's two of them. But the kicker is that these aluminum leads are also thermally conductive, either into the package towards the junction, or away and into a generous PCB layer or to suitably-sized copper wires.
Either way, that will sink a fair amount of heat, although the thermal resistance for the package legs is not given in this datasheet. It may be defined for generic TO-220 packages though.
As a practical matter, to operate a MOSFET ar 120 A would likely require active cooling, and their test jig plus all reasonable implementations will have a fan. Moderate airflow over the leads will also wick temperature away, which might bring the leads down to a "hot but not fire-inducing" levels. But an EE or thermal engineer would need to sit down to do that simulation.
It's worth keeping in mind that metals can get quite hot and still maintain their structure, although the NEC (electrical code in the USA) ampacity charts would suggest that 14 AWG (~2.5 mm^2) is only good for 15 A. Building wiring is a different beast, and those charts are written by fire engineers, whose job is to avoid the preconditions for house fires. Hence, extremely conservative for temperature rise. Whereas electronics in a metal box with active airflow can take substantial liberties with metal's current carrying ability.