The translation is correct English. "Them" in this case is an indirect object. You don't use "to" with indirect objects. E.g. "Please give him the money." "Money" is the direct object, and "him" is the indirect object. Of course you could also phrase it, "Please give the money to him," and then "him" would be the object of the preposition "to". Either way, with or without the "to", it means the same thing.
So the phrasing you suggest for Camus, "... had been given to them to lead," would be just fine also. Maybe the translator didn't like the sound of the 2 "to"s so close together? Whatever his reason, his way works too.