The only influence to speak of was probably when those demigods realized that the item in Zhou Tian's hands was a Demonic Slaying Weapon, they naturally became much more cautious in their combat against him. After all, even though the disruptive ability of the Demonic Slaying Weapon did not affect them as significantly as it did domain powerhouses, it did not mean that the Demonic Slaying Weapon posed no threat to them.
Once strength reached the level of a demigod, in theory, it is very difficult for it to wane, and even the demigod Zhou Tian had previously killed did not lose his life after being defeated by Zhou Tian. Had it not been for Zhou Tian's possession of the Demonic Slaying Weapon, the demigod might have escaped in the end.