It seems the gift was the language which allowed one to see the future, but Abbott and Costello gave this to Louise.
Abbott and Costello were the aliens in the Montana ship. They gave it to Louise because she was the human they were interacting with. Aliens in the other ships would've been trying to give the same information to the humans they were interacting with, and may very well have succeeded too; we just don't see it on screen.
Why would they do this if they intended all nations to work together in order to get it?
As above, the aliens in all the ships are working towards the same goal with the humans they're talking to. Louise is just the one who got there first.
The aliens want all of humanity to work together because they need humanity to survive the next 3000 years without obliterating ourselves. But that doesn't mean that everyone needs to figure it out at the same time - just that the gift be transferred to humanity in general (which Louise ultimately does by publishing her book on their language.)
What prevented the scientists of other nations from getting it as well?
Nothing. For all we know, scientists in some or all of the other nations did figure out the language as well. The movie sticks with Louise and her team, so we don't really see what the others did or did not learn by themselves.
I certainly don't recall anything suggesting that people other than Louise failed to learn the language. It seems like the Chinese general probably didn't learn the language himself (based on his saying "he can't understand how [Louise's] mind works" in their meeting 18 months in the future) - but he's just one man. All that tells us is that he, personally, did not take the time to learn this new language. Other people around the world may very well have done so by then, for all we know.
Edit: Ian probably didn't learn the language either, otherwise he wouldn't have needed to be told what would happen with their daughter.