I would go off it the max wattage of the power supply the whole system uses instead of what the laser says.

That will have you covered for peak draw over the entire duration you're looking for, and will likely end up giving you a lot of wiggle room time wise.

I know almost nothing about laser engravers, but many of them are mechanically similar to 3D printers, which I do know a lot about, and stepper motors can suck down a lot of power.

More directly answered, most CO2 lasers are rated in optical output power. There are a lot of inefficiencies before that, so e.g. the 85% efficient power supply, the (wild-ass-guess) 40% efficient laser, then you have other electrical loads like probably at least a dozen watts of fans, substantial power for motors, lights, controllers, air pumps if you have one...

I would expect a "120w" CO2 laser to have peak power consumption of at least 500w. You can use a kill-a-watt to check out the actual consumption while cutting, frankly I'd probably go with a 750-1200 kVA ups just for substantial fudge-factor.

Curious if you've already bought the UPS and if so how it's gone?