The Word Which

Hi, I have a grammar question. I wanted to quote a sentence, or at least half of one, from a well-known writer. Given the inappropriateness of its subject matter and its irrelevance to you being able to answer the question, I will omit the first part of this sentence.

"—and an enormous serpentine line of fans with cameras and autographable memorabilia has formed at the Impressive booth, which line Ms. St. Claire appears for the moment to be ignoring …"

The part of the sentence I'd like to focus on is ", which line." Why isn't it "a line which?" There are countless examples in which this writer does this very thing. He was extremely ridged about grammar, so I very much doubt it's wrong. And maybe I just haven't been doing enough reading, or else not enough attentive reading, but I don't remember other instances of this order of words from other writers.

Can somebody explain? Thank you.