Has a governing body issued you a license, without which one cannot practice your profession? No? Then indeed, you are not an "engineer" in the sense of a
profession, as with doctors and lawyers and CPA's, etc. This is wholly orthogonal to the prestige of whichever college you graduated.
Note that even on your own Stanford and MIT links above, they reserve the term "engineering" for programs OTHER THAN "Computer Science" (e.g. "Chemical Engineering", "Electrical Engineering", etc). Show me a "Software Engineering" program at any accredited university.
There's no confusion, I am 100% talking about PE regulations. One requires a license to practice chemical engineering, electrical engineering, mechanical engineering, all but the most entry-level roles in aerospace engineering, etc. Employers effectively cannot hire non-licensed workers for those positions.
If that does not apply to your job, then you are an "engineer" only in the sense of LinkedIn puffery.
Mind you, this applies to all us (myself included) in the software development field. I'm not trying to be a gatekeeper. Rather, the complete absence of gatekeeping is the entire point here.