While I don't actually know, I did some digging and found one interesting theory over for it here at the Online Etymology Dictionary, specifically:
Meaning "one's occupation, branch of business" is from 1630s, probably from misunderstood KJV translation of 2 Cor. x.16, "And not to boast in another mans line of things made ready to our hand," where line translates Gk. kanon, lit. "measuring rod."
Just reading some alternative translations however, it looks like the general consensus for that line when they've tried to rephrase it is "...not to boast about what another man has done..."
(have a dig through a couple of versions at the Bible Gateway if you're curious, for example, the Common English Bible version of that line)
Unpacking the process, it doesn't look particularly crazy, the KJV is quite an influential text for a start and the passage in question looks like it has been translated oddly if the modern translations are correct(er). If that was the case back in the day, I'd not be surprised since the verbose explanation of the passage would pretty much be talking about the things someone is doing (or more pointedly - his work) and the existing meanings of 'line of' would need to be augmented for the sentence to make sense (hence, a new layer of meaning).
If the theory is correct (and it sorta makes sense to me, but again, grain of salt since I'm not doing particularly deep research here) the usage you're talking about could've come from this as line-of-business refers to what you actually do, so your mission critical software almost by definition is what falls into that category whereas your ancillary software might not.
If I had a time machine to go back and tweak it to "...not to boast in another mans area of things..." we could see. Lacking such a machine though I'd need to do some proper digging to move this theory past the 'crackpot, uneducated loon' stage. I'm hoping someone else might have more insight or suggested sources - particularly if I could nail down an upswing of the phrase in this usage about the time of the publication of the KJV bible + a couple of decades, I'd feel a lot more confident.