Have I erred in declaring someone an unbeliever who said, "I am the god of Babylon," and do I incur disbelief in this case?

The correct approach would have been to say to the one who uttered a statement of disbelief (kufr), "This is disbelief," instead of "You are a disbeliever (kafir)." This is because judging the act does not necessitate judging the doer, due to the presence of a barrier such as misinterpretation (ta'wil). Furthermore, one who says to his brother, "You are a disbeliever," does not become a disbeliever himself. If the addressed person is truly a disbeliever, then the matter is clear. If he is not, then the one who said it is either misinterpreting or ignorant. The Prophet, peace and blessings be upon him, excused Umar and Mu'adh when they accused Hatib and the man who prayed briefly of hypocrisy, because they were misinterpreting. And whoever declares a Muslim a disbeliever based on a permissible misinterpretation does not deserve blame. However, one who believes a Muslim to be a disbeliever without a disbelieving cause becomes a disbeliever. But if he says it with the intention of insult, without believing it, he does not become a disbeliever.