The Spirit Stream wasn't something created by the spirits, though. It had been there way before the spirits took control of this side of the center of the Realm of Gods. In fact, the Spirit Streams extended way beyond the center.
Unlike the humanoid races' territories, the spirits did not have any border between the center of the Realm of Gods and the far away continents. Any spirit that had the ability to do so could come to the center of the Realm of Gods at any time.
In fact, the same thing happened in the demon beasts' territories. It's just that, as demon beasts, they were a lot more 'territorial.' That meant any demon beast trying to take place in the center of the Realm of Gods would need to win that spot through sheer strength.