Of those choices, vector is clearly the more correct one.
Here is what a constructive response would have looked like:
"Lisper is correct when he says it's a vector and not a "magnitude" (the more common term is "scalar"), but there is an important subtlety: it is not a vector in 3-D space. Instead it is something called a spinor (https://en.wikipedia.org/wiki/Spinor) which is a kind of vector, but behaves differently than vectors in 3-D space in some important ways. For example, if you rotate a spinor 360 degrees you do not get back the same spinor you started with. You have to rotate a spinor 720 degrees to get back to where you started.
And in fact if you really want to get into the weeds, in the mathematical formalism of QM these are actually things called "rays" in something called a "Hilbert space" but no one cares about that, not even physicists, which is why all physicists refer to these things as "state vectors" rather than "state rays" even though there are some formal differences between vectors and rays. But only people who want to publicly exhibit their superior knowledge (as opposed to engaging in effective pedagogy) would ever bring up such trivial details."
How? Take people's word. If they say vector, assume they just mean some element of a vector space. No need to be rude to somebody based on an assumption.