I'm afraid I find the given translations frustratingly random! As a UK native speaker of English I have to guess americanisms, which I can do, but then find there is no consistency. 'We will go work' was given as a model answer previously in this unit, whereas ' the men will go work' is not accepted here!!
I believe it's the "work" verb which is causing confusion here, because it carries the idea of going somewhere to work within it.
Do you ever say "I will go eat"? Is it the same as "I will eat"?
If it is, then you are right, if not, keep reading.
Well, what I'm going to say is not a strict rule, it's very flexible indeed. But...
See that "vão" means go if it's in the present. (go from a place to another place)
But when it is making the phrasal future, it loses the "going" meaning, which is changed by "will".
So, this sentence can have these meanings:
1 - The men go work (they travel from a point to another in order to work)
2 - The men will work. (no movement here, just future)
3 - The men are going to work (leaves the same doubt as in Portguese, "present going" x "future working")
But "the men will go work" involves both movement and furute. So, in my opinion, it needs "ir" in the future tense: "Os homens irão trabalhar"