It means that people should know the history and culture surrounding Kipling and The Jungle Book, simple as that.

...you have no idea what “context” means, do you? It means, we should know the history and culture surrounding something even when we read or watch it. It’s Reading Comprehension 101 - you better understand something the more you know about the context in which it was written.

The article isn’t stating that about The Jungle Book either. Read the article and not just the title: it’s stating that we need to place Kipling and the book in their proper context.