The article claims that the usual explanation— that it's caused by nervousness or low self-confidence— is a crock. And then in the section on positive conditions it says that stuttering can be eased or increased by circumstance, such as the stress level of the speaker. Which is kind of the same as saying it's nervousness. I suppose the point is that the underlying mechanism is neurological, not psychological, and then the condition can be modulated by circumstance.
I guess Giles, at least as I'm writing him, would qualify as a non-chronic stutterer. My Giles doesn't stammer when performing magic. The usual analysis of canon Giles has him stammering a lot when he's new to Sunnydale, then less as he becomes more comfortable with the Scoobies. I'll probably stick to this. I can probably also work with the idea that he's frustrated by the stammer, and embarrassed by it.