The revision that changes the sentence to draw attention to the object of the action rather than the people performing it is the one that reads as follows: "'The space race' was a cold War competition by scientists". This is the case because the NP "the scientists", denoting the ones performing the action, has been introduced by the PP (prepositional phrase) "by".
The copular verb "to be" used in this sentence takes an NP predicate which tells something about the subject ("space race"). By making "space race" the subject of the sentence, you highlight the fact that the race is the most important information in the sentence. The PP "by scientists" describing the ones performing the action could simply be dropped and the sentence would still make sense and be grammatically correct: "The 'space race' was a Cold War competition".
If you want to make information clear to your reader, it is often useful to place the old (or known) information at the beginning of the sentence
. On the contrary, the new (or unknown) information is placed at the end of the sentence. Perhaps, you can infer that the "space race" was a competition ran by scientists and that is why the writer has chosen that structure.
