It’s correct, and as Simon Déchamps says, your rearranging of the phrase is also correct and is the right interpretation of what it means.

The key lies in the fact that you can say que or qui in places like this. And que would have to follow the object of the verb, but qui would have to follow the subject of the verb.

This is important because languages that let you mark syntactic roles like subject and object usually have more variation in word order. French doesn’t have many cases like this, but in languages like Latin and Russian, word order is extremely flexible because it doesn’t change the meaning.

Therefore, since the meaning is safe, a person can choose word orders that make the reading a little easier (to a practiced eye), or that change the focus of the sentence.

In this case, there are two reasons why you might want the verb before the subject. One is that the subject could be long but the verb short. As I mentioned in this answer, shorter elements tend to be put first to get them out of the way — when you have the freedom to move things around.

The second reason is that this is a subordinate clause buried within the outer clause. If you used the regular order, you would get two verbs in a row: possèdent joue. The first one is from the inner clause and the second one from the outer clause. But two verbs in a row could be confusing for the listener.