An important test case for considering whether Islam is a Christian heresy is to consider whether Mormonism can be called a Christian heresy. Both profess all sorts of doctrine which is completely incompatible with any common Christian teaching, but at the same time both have their roots in Christian thought. Without the Bible there would be no Quran and no Book of Mormon.
The sticking point for me is whether we must consider followers of a Christian heresy Christians. At first it might seem like we obviously should, but imagine a world where the Gnostic heresy had not been quashed and was still a major part of today's world. Its doctrines were incompatible with Christianity and if they had been allowed to develop further would almost certainly have moved further from their source, to the point where it would be absurd to call a modern Gnostic a Christian. Yet at the same time Gnosticism has always been considered a heresy of Christianity. It is in this sense that we can consider Islam (or Mormonism for that matter) a heresy.
A heresy is marked by its perversion of its source, and in particular the way that it attacks the doctrine as a whole by emphasizing or increasing special features. The word "heresy" even is derived from the word for "choice;" a heresy "choose" part of the truth to destroy the rest. So the gnostic heresy choose the truth that our spiritual concerns should be foremost, but distorted this into a teaching that the material world was evil (eventually even calling God, or at least actions of God, evil). Similarly Pelagianism took the truth that the free will was good and distorted that into saying that it was so good that man did not God's aid, Donatism took the truth that we should strive to be saints and distorted that into a requirement that the Church be run entirely by saints, Arianism took the truth that God created all things and that Jesus was a man and distorted that into a teaching that Jesus was a created being, and so on. After the distortion what remains often does not resemble where it started from.
Islam chiefly differs from its emphasis of God's supremacy. It is true that God is supreme over all and has authority over all, but Islam cannot bear anything which even seems to question God's authority (even if it does not). So they cannot allow that God took the form of a slave, because such a form would not be fitting for such a supreme being. But at the same time, they cannot consider the hypothetical question of whether God could do evil in principle (but in practice does not), and avoid it by saying that whatever God does is good simply because God does it. Likewise there has never been the support for applying reason to theology, because to suggest that God could be understood even partially by human reason would be to bind Him to it (at least from the perspective of Islam). There is even a resistance to allowing there to be secondary causes in the world, because that would deny God the opportunity to be the only cause of all (and thus the teaching of occasionalism took root). All of these things initially seem disparate, but they have their origin in a single twist of Christian doctrine.
Saying that Islam is a Christian heresy is not really doing it much in the way of favors. In fact, if it is, it is more blameworthy for them to be ignorant of the truth, as compared to practitioners of wholly separate religions. From what little Chinese history I know, it would not surprise me to learn that Confucianism was far more receptive to Christianity, despite having fully distinct origins. I would also say that it does not necessarily mean that they are closer to Christianity or more receptive towards it: it is a statement of origins, not of current or future locations. There are times when Islam had some possibility of reconciling itself with Christianity, especially when it takes philosophy and reason seriously (such as the time of Avicenna). But due to its core nature it cannot bear such trends for long and in the long run will likely remain a bitter enemy of Christianity.
