Chinese Wikipedia https://zh.wikipedia.org/wiki/%E7%94%98%E8%82%83%E7%9F%BF%E5... has the coordinates. It's a lot closer to 玉门 than to 嘉峪关.
I don't know if those coordinates are correct. They seem to be the exact coordinates of Jiayuguan City [0], but then the article also says that the 404 site is located "100 km west of Jiayuguan City," with living areas later relocated to Jiayuguan. So I think the article authors just put the Jiayuguan coords there.