I feel ambivalence about the use of "engineering" in software. We do have "sound engineers" and "special effects engineers", consistent with a vernacular use of engineering to mean "the ingenious use of technology" (made up by me). Within that context, the term software "engineering" really isn't especially outrageous. I think that the public is not threatened by this use of the word, since they are not confused by the difference between a sound "engineer" and a licensed structural engineer. However, software "engineering" could slip into that grey area.
One thing that makes me worry less is the restructuring of the FE exams to reflect the body of knowledge in the various fields. For instance, Industrial Engineering is now substantially different from Mechanical even at the FE level. Another interesting thing I learned is that certain fields are just title based - I believe that this means you can't represent yourself as an "Industrial Engineer" in a professional context if you aren't a PE, but there isn't a practice restriction (at least that is how I interpreted it, because I don't do either it doesn't really affect me).
But one other thing I would like to mention - while I phrased my argument in the context of not wanting PE to gain control over software licensing, I do agree with you about the term "engineering". I do agree that you should have a background in those things you mentioned to be using the title where "engineer" implies this sort of background, and it is hard earned.
So I'd agree that software engineers may be grabbing a title they don't really have rights to, though I would still argue that software has far more in common with math (even math theory, like abstract algebra) than heat and mass transfer.
Oh one more thing - your description for the intended use of "software engineering" as "formally trained engineers who are working on software-intensive projects" sounds reasonable - it covers software for specific engineering systems. My worry is of scope creep - the initial process is limited, highly relevant, and justified, but it later morphs into an "I'm licensed and you"re not" situation. If that happens, I'd almost want to see some math body establish a degree requirement and math background (including things like abstract algebra and real analysis), along with very intensive algorithm questions, as a counterbalance (au contraire, mon frere, you're not licensed).
I read Milton Friedman's bit on "abolish the AMA" and enjoyed it, but ultimately, I support limited licensing and credentials to protect the public - however, I do feel that scope creep really is a serious risk here.