"Does this mean that they wish they could see the food again?" No.
That would be: Die Männer vermissen das Essen.
vermissen : to be missing, to lack
verpassen : to miss out, to overlook
Well "verpassen" refers to miss something like an appointment or a date (or even a chance). It has to do with time overlapping between what you had in mind and what actually happend. If you miss the bus, hast du den Bus verpasst. Fehlen is a thing or person gone missing. I miss my cat : mir fehlt meine Katze. (because maybe you're on a trip and the cat is at home) And to top the confusion, there's "vermissen" as in longing for (a return). I miss my cat could mean : Ich vermisse meine Katze (because she died)
In my understanding "fehlen" refers to a personal state of being, while "verpassen" refers to a set of circumstances.
A waiter might ask "Was fehlen Sie?" or "Fehlen Sie etwas?" It is closer in meaning to the verb "vermissen."
Verpassen would be used in something like, "Ich habe dich am Bahnhof verpasst," or "Ich habe die Folge verpasst."
Does "verpassen " also mean "skipping a meal"? Can I say =Ich verpasse Schokolade essen=I miss eating chocolate (I have stopped eating it and I miss it) oder Ich vermisse Schokolade essen
Ich habe das Frühstück verpasst oder Ich habe das Frühstück ausgelassen? (ich habe kein Zeit)
If you say that, it could imply that the men are present at the meal, but aren't eating for some other reason, or are only skipping a particular course.
If you say that they're missing the meal / the food, it implies that they aren't present - they're stuck in traffic, or have decided to go to a movie instead, or something.
"Vermissen" seems to be a little better than "fehlen" if you want to express missing in an emotional sense, too, but I'm not certain on that one.
edit: I wanted to strike part out because it's wrong (more honest than just editing and deleting), but apparently we can't do that on Duo even though it's meant to be using markdown. Ignore it unless you want to follow the conversation: Close, but you've mixed the cases. That expresses that the food misses the men. You'd need "die Männer" in nominative, and "das Essen" in accusative (which doesn't make a difference in this instance). Normal usage would also swap the positions of "das Essen" and "die Männer", but your way is also understandable.
Because there is food, but the men are missing it. It's in sort of the same sense as how you'd miss a train. They're not missing it emotionally, or lacking it the way that my torch is missing batteries. Maybe the businessmen are missing out on the "lunch" part of their lunchtime meeting because their taxi to the restaurant is stuck in traffic. Maybe Jeff and Robert are too wrapped up in the superbowl to get up and make themselves burgers in the kitchen, and it looks like the food will be all gone by the time they get there.
"The men are..." is a little stilted, yeah, but plenty of English speakers would say something like "hey, the guys are missing the meal" in those situations, and others along those lines.
Because the German just says that they are missing the meal, but not why. Maybe they did forget it. Maybe they tried to get there on time, but missed it because they were stuck in traffic. While I'm not a native speaker of German I'm fairly sure that "vergessen" isn't synonymous with "verpassen", so we should just go with what is explicitly said, which is just that they missed it.
Fehlen is like when you miss somebody or something, usually because it isn't there. Your boyfriend, your mother's food... (n.b. I'm not a native speaker, so there's a chance I've missed something important about the contexts in which you can use fehlen somewhere along the line. But this is the general idea).
Verpassen is like when you're running late and miss your train.
I never realized until now just how imprecise the word “missing“ is in English. The above sentence could mean the men forgot to include the food, are pining for the food, are late to the meal, or are taking inaccurate potshots at the food! Maybe even assigning unmarried female status to the food. ;-)