Christian Science is not 'gnostic Arianism', though it may appear that way. It's not 'gnostic' since, well, no one has yet defined what 'gnosticism' actually is, so until someone does, I'm standing by my statement that CS is not 'gnostic'. It is not Arian, either, since Arians believe that matter exists.
CS teaches that matter does not *really* exist, because Spirit, or God, is the only Reality. Sure, you *think* matter exists, but that's because your perception is clouded by the delusion that matter *really* exists. Jesus was the primary Teacher of this "All-reality-is-God" idea, and the second coming of Jesus Christ is actually the re-discovery (by Mary Baker Eddy) of Jesus' True Teaching.
CS has some similarity to the Hindu school of Advaita (or "Non-Dual") Vedanta, which has similar views of the "reality" of matter, but Mary Baker Eddy most likely was not influenced by Advaita. Her primary influences may have been (1) her reading of the New Testament; and (2) the idealism of Western philosophical traditions (like the Transcendentalism of Emerson).
However, one could call CS a sort of Christian Theo-monism, monism being the belief that reality is actually one "thing", in this case, reality is actually Spirit, or God.