I thought it was hilarious for the same reason, but I don’t think anyone in Chinese refers to that book as 小红书. It’s the 红宝书. I’ve never been to China and perhaps google/Baidu/Pleco isn’t going to perhaps pick up that kind of usage, but I think it is more of a cross cultural accident.
The article is about a bookstore in Manhattan, called “Little Red Books” though. Your link is an abbreviated translation of this article, which you might notice from the link at the bottom. I don’t know if that serves as the kind of linguistic evidence that’s called for here.