Nein!

Right the first time really.

"non-IT news related story" implies it is a "story" not related to "IT News"

"non-IT related news story" implies it is a "news story" not related to "IT"

since the article is a "news story" (a telling of recent factual events), rather than a "story" (a narrative piece of writing either fiction or non-fiction, not necessarily recent in either case), the original grammar works best.

For more insight please read my latest book:

Mein Kampf (gegen die schlechte Grammatik)