The spider-like description is sometimes used to describe the crawl, but sometimes there no mention of crawling...just spider-like movements.
People seem to have difficulty explaining it. Whether that's because it's just so strange to see a bipedal mammal move like this or because they are just latching on to an interesting description that they previously heard and don't know what else to say, I don't know.
Certain tropes seem to get popular and are then commonly adopted in witnesses' accounts. The first time that I ever heard about spider-like movements was Wes Germers encounter. Then, it seemed to start popping up periodically.
You just keep hearing that same description.."it moved like a large spider", but no one seems to go into any greater detail.
I imagine that it looks something like this.