That depends on which book you believe.

Islam talks about all of the previous prophets including Jesus, whom it says was not actually the Son of God. Whereas Christianity has the Trinity concept, Islam addresses this and means to restore the emphasis of divinity on God himself.

If someone is a Christian then of course he/she will not agree with this. But to a Muslim or even to a non-believing observer who might read the texts but not form opinions on what is true and not true, the Islamic God is the Christian God.

Of course it does. If you hold to the Qu'ran and the Hadith, you will deny Trinitarianism. If you hold to the New Testament--and your exegetical approach is roughly consistent with that of historic orthodox Christianity--then you will hold to Trinitarianism. That's precisely the point that I was making. For anyone, Muslim or otherwise, to claim that the Islamic God is the Christian God, is both arrogant and fallacious. Religious communities must be allowed to define their own beliefs. Muslims would be highly offended if Christians went around claiming that Allah is a Trinity, so it is similarly out of bounds for Muslims (or anyone else, for that matter) to claim that the Christian conception of Yahweh/Jehovah is not Trinitarian.

Marcion Of Sinope thought Yahweh was just a Demiurge and not the true God of peace, love and knowledge but saw himself as a Christian.

True, he did see himself as a Christian, but the community of faith itself disowned him. Again, you must allow communities of faith to define their own religious beliefs. Marcion was ruled a heretic and excommunicated because his beliefs were more in line with Gnostic philosophy than with Christian doctrine. That Marcion's allegiance to Christianity is questionable is also evidenced by the fact that he had to establish his own stripped-down New Testament canon in order to retain his peculiar viewpoint.