Just because Jews and Muslims don't recognize God as their God doesn't mean God has no no domain over them. God is still their God regardless if they hold Muhammad or themselves as idols and they will be judged accordingly.
God was still God over the Canaanites, over Egypt, over Babylon, and even over the disobedient Israel. God is still God over Mormons, God over LARPagans, over Communists, even over satanists and Satan himself.
Just because they fail to recognize God's authority doesn't mean God isn't their God. Just because schismatics fail to recognize the See of Saint Peter doesn't mean Saint Peter has no authority.
How does sedevacantism make any logical sense?
Jews and Muslims DO have the same God. What they lack is the Spirit currently working with them. This is why he's so impersonal and distant from them, despite having the same core of beliefs. And why Christianity is so fulfilling once they convert..You'll hear it from any Muslim or Jewish convert. That they never thought of God in such personal terms before.
But they do indeed have revelation of the same God. It was the Word of God himself who appeared to Abraham and Hagar. They just lost touch.
As for the rest of people, that's wrong. They don't even have revelation. At best, the wisest ones know that they don't know. Like Paul, when he reached the Greeks - he didn't say something retarded like modern Catholics do.. how all of these Greeks "essentially" believe in the same God. No, he spotted the shrine to the "Unknown God" then preceded to tell them how ignorant they all were and this was the only thing they had right.