Perhaps I'm picking nits here, but Arius, while he taught some of the beliefs of Gnosticism, simply didn't teach that people were saved by SECRET knowledge only for the elite, and THAT is the defining characteristic of gnosticism.
It's been a long time since I visited the conflict over Arianism in the church (When Jesus Became God, by Rabbi Richard Rubenstein -- fantastic book) I don't remember it comparing Arianism to gnosticism. I had to look up the topic on the net. From what I could find, Arius was a successor to the Gnostics, but was not actually a Gnostic.
I agree that Arius didn't specifically teach salvation by knowledge but he was a part of the Trinitarian enterprise. He was an elder in a Trinitarian church.
Arianism was not so much a Christian heresy, as a heresy within High Trinitarianism itself, which does teach that knowledge of "God the Son" is paramount on pain of anathema.
I agree that Arianism doesn't brand Jesus an illusion, as with docetism. By focusing on Jesus' humanity, it even downplays Trinitarian gnosticism. In fact Arianism seeks to make High Trinitarianism less gnostic than it actually is, by allowing for subordination of Jesus to his Father. But it was misconceived because it made the terrible error of making Jesus out as less than fully divine. The truth was that Jesus was not "God," because God infers having the attributes of God as well as the identity of God, but Jesus was divine in that he came from nothing less than God.
High Trinitarianism has put many to death, including conversos, for not "knowing" that God begat a son "in heaven." Thus Michael Servetus was put to death for not owning "God the Son" although he owned the "son of God."
God the Son is gnostic (knowledge based)
Son of God is biblical (faith based)