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)
- Review Apple iPhone 6: Looking good, slim. How about... oh, your battery died
- Review + Vid Apple iPhone 6 Plus: What a waste of gorgeous pixel density
- +Comment EMC, HP blockbuster 'merger' shocker comes a cropper
- Moon landing was real and WE CAN PROVE IT, says Nvidia
- 46% of iThings slurp iOS 8: What part of this batt-draining update didn't you like?