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)
- +Analysis Microsoft: We're making ONE TRUE WINDOWS to rule us all
- Apple: We'll unleash OS X Yosemite beta on the MASSES on 24 July
- Pics It's Google HQ - the British one: Reg man snaps covert shots INSIDE London offices
- White? Male? You work in tech? Let us guess ... Twitter? We KNEW it!
- Apple fanbois SCREAM as update BRICKS their Macbook Airs