This practice varies. Some of us were taught to speak a certain way, which agrees with the written rules. The rule is that people get it, and animals you love or other things you love and tend to personify (like your country sometimes) get the personal a. However, in practice, some people throw the personal a around a lot more in cases that don't follow the rule.
It's a matter of preference to some, it seems. You now know (my English paraphrased version from memory of) the rule on paper. The question is, how much of language is rules, and how much is just use (as long as the speaker and listener both understand each other)?
My opinion is that rules matter because they help preserve language enough for us all to understand each other, but the language exists for the people to communicate, not to limit them with arbitrary rules. In the case of the personal a, neither way will prevent the message from being understood. I'll use it the way I was taught, because that's how it is familiar to me. Also, speaking according to the rules helps people who aren't as familiar with the language. It's hard enough understanding a foreign language when spoken according to rules. Maybe I'm more careful because I've had to work around people who weren't very familiar with either Spanish, English, or both in some cases.
If there is no additional context, especially in Duo, it's safe to assume that if they use a possessive adjective "su" or "sus" - it will usually belong to whoever was already mentioned in the sentence.
Since they used "ellos", "sus" is probably referring back to "them/theirs"
If they wanted this one to be "his" it would probably be phrased: Ellos derrotan a los enemigos de él.
That being said, your answer is technically correct too since "su" can mean his/hers/its/theirs. Report it.
The direct object pronouns usually replace the direct object, while the indirect object pronouns are (in most sentence constructions) required, regardless of whether the indirect object is actually stayed. In other words, if they state what the direct object is, you don't need the pronoun. Indirect objects are different.