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)
- The land of Milk and Sammy: Free music app touted by Samsung
- The long war on 'DRAM price fixing' is over: Claim YOUR spoils now (It's worth a few beers)
- Privacy warriors lob sueball at Facebook buyout of WhatsApp
- Dell thuds down low-cost lap workstation for
cheapfrugal creatives or engineers
- 20 Freescale staff on vanished Malaysia Airlines flight MH370