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)
- +Comment Anti-Facebook Ello: Here's why we're still in beta. SPAMGASM!
- NASA rover Curiosity drills HOLE in MARS 'GOLF COURSE'
- Video and pics Microsoft reveals NEW Windows 10. WAIT, 10? Yes, 'cos Seven ate Nine
- WHY did Sunday Mirror stoop to slurping selfies for smut sting?
- Business is back, baby! Hasta la VISTA, Win 8... Oh, yeah, Windows 9