Personally, I would only engrave an unplated solid brass or sterling silver zippo. I'm guessing the one shown is plated, and possible brushed chrome. Or silver plating over chrome.
i just finished 3 zippos this week. 2 were real brass, 1 was chromed. the reall brass ones engraved nicely by hand. the chromed one i did on my pantograph. anything that's plated, can chip or flake away from the cutline. it's a coin toss if it will turn out ok. contact the zippo company. i'm sure they would give you info concerning this model lighter.