It's like how you use causative(make, let, have) in English. The sentence(没有分开他们) still makes sense if you don't write the 給.

the action 分开 doesn't come from "它们", we dont know where it comes from, maybe some people. In this case, we dont care who did this action, we just care the result of this action, so we add 给

也可以说“因为没有把它们分开”或“因为没有将它们分开”，“给”相比“把”和“将”，多了强调“它们”的意思，所以这里用“因为没有给它们分开”的确是最好的

可以说“因为没有分开它们，大鱼吃了小鱼”，不过“给它们分开”更好，因为强调分开的动作。