This is a problem of the rewrite rule in the wiki article and not a bug of DokuWiki. The rewrite rule redirects the CSS requests to HTTP and Chrome doesn't load unsecure content in secure pages. The proper solution is to enable HTTPS for all requests.
I partly disagree with the comments about closing. I agree that it's not a bug in the DokuWiki core, but it is a "bug" in the documentation of that page. Either that page should include how to always send the CSS over https, or at least it should explain this very issue.
So, I would re-open and change the category to "Docs"?