thought in order for one to call themself a "Christian", one had to believe that Jesus Christ was the son of God and that he died for the sins of mankind. Am I wrong?
Many Orthodox Christians would agree with you. They would deny my claims to be being a Christian, but that's all right. Christianity is just a word, it doesn't matter whether I call myself a Christian or a pagan. To me, being a Christian means following the teachings of Jesus, not just putting faith in him. I have faith in the example he showed, and his teachings on love and returning to the Pleroma. There is no need to believe in the historical person of Jesus in order escape the judgements of an angry tribal god, we were never under any sort of eternal condemnation to begin with. Gnostics do believe that Jesus was the son of God, or One with the Father, however it is something that all gnostics aim to one day achieve.
Do Gnostics call themselves "Christians" even though it appears as though they don't believe in the same "Christ" as the Jesus Christ of the Bible?
Well, there are Gnostics and then there are Gnostics. Not all of them are the same, Gnosticism existed before the events in the Gospels. Many Gnostics did not personally follow Jesus, although they did agree with his teachings. Christian Gnostics, such as myself, do believe that there was a teacher named Yeshua, though the description of his life in the Gospels may not all be literally true. Many Gnostic sects held a dualistic notion of reality. They believed that matter is evil and only spirit is good, which IMO is a horrible mistranslation of what Yeshua was trying to say.
Do people who believe in a "spiritual heavenly Jesus", believe that Jesus ever walked the earth?
Many mystics do believe that there was a teacher, or a group of teachers, in ancient Palestine around whom the story of the Gospels was developed, that he became an incarnation of the Logos, performed various miracles and was executed. However, it is the essence of the heavenly Christ that is most important, not the person of Jesus. Whether or not the events of the Gospel literally happned is quite beside the point.
The early esoteric Christians, wanting to bring about change within the corrupt, legalistic Jewish religion were trying to transmit the knowledge of the many Greek mystery schools that existed at that time. They could have chosen the example of the master Yeshua, one of the foremost among them, and used him as an allegorical example of the deep concepts they were trying to express to the Jewish people. The story of Jesus's suffering on the cross actually has a strong pantheistic theme, basically that we are part of God, God suffers along with us, and it is through suffering that we are purified.
The heavenly Christ is not confined to the historical Jesus, it is our higher self/inner angel that is within all of us. By dwelling in love, the inner Christ fills the heart of the believer and changes them from within. This is what the scriptures mean by being washed clean in the blood of the lamb. This can happen to people of any religious background, even atheists, though they may different ways of describing it.
Part of the reason I choose mysticism as my current understanding is becuase the esoteric path has been held by thousands of groups over thousands of years, with a very high level of consistency. Buddhism, Gnosticism, Essenes, Taoism, Hinduism and Shamanism have all held very similar beliefs which can be backed up through personal experience. The same cannot be said of the orthodoc monotheistic religions.