I think the computer program is wrong in this instance.
You should write "WHOSE government is. It is wrong to write "thats" government is, and it's also wrong to write "that's government is."
If you don't lilke "whose government" -- because Darfur really is an "it" and not a "who," you could make two sentences here and avoid the awkward use of the possessive pronoun.
"Darfur is a region of western Sudan. ITS government is ..."
Explanation: There is no such word as "thats," that I'm aware of.
There is such a contraction as "that's," but it only means "that is." It never means "belonging to that," as far as I can remember from English class.
THAT in this sense is very different from IT.
The proper way to use "its" and "it's" is without parallel anywhere else in the English language.
We write "it's" to mean "it is," but when we want to say "belonging to it," we write "its," in order to distinguish this word from "it's" meaning "it is."
Every other singular possessive that I can think of, however, uses an apostrophe "s" to indicate "belonging to."
The President's speech, the woman's hat, the man's jacket, the child's toy, the burglar's gun, Frank''s car, Mary's amazing boyfriend, her boyfriend's amazing muscles, Betty's prayers to God, and so on.
In the case of "that," I believe that English writers just don't make a possessive out of it at all. So I would write "whose government," even though that doesn't quite sound correct, either.