The goths were Christians, just heretics.
Well, not just any heresy; they denied the Trinitarian nature of God which is enough to put one outside the pale of orthodox Christianity. For a similar reason, Jehovah's witnesses, Mormons, and other like-minded quasi-Christian sects that do not accept the Trinity are not Christians. What one believes about the nature of Christ is THE game changer, as the efficacy of our salvation depends on it. If Christ was not true man and true God, he could not be the One, essential mediator between man and God.