I would say that the "here" part is implied in english "come quickly". It's a phrase I've only ever used when I meant "come here, to where I am, quickly", and can only ever imagine it being used to mean that. "Come here quickly" seems a bit redundant to me in English, since the implication of the word "come" in the sentence is to move towards/to the speaker (which is where "here" would be). Personally, to me, "come here" and "come quickly" sound like good sentences in English, but "come here quickly" just sounds really odd and strange to me.
I'm a typical English speaker and I have no problem with here. But even if it were a little odd (but not incorrect) I'd keep it in as it helps to learn Swedish -- the purpose of this course. I think the Swedish commentators have done an amazing job of balancing the need for conveying an understanding of Swedish sentence structure and word usage in their translations with using idiomatic English.