Of course we are engineers. OP uses "building a bridge" as an example of 'real' engineers. This is patently ridiculous on the face of it.
The one thing that unites us is we like to build. Whether it's the great pyramids or the latest social network, engineers are the ones who get it done.
We build. That's what engineers do. We build something to solve some problem whether it's with bits and electrons or with larger physical mediums like slabs of concrete. Engineers are builders and they build to solve some particular use case.
"Scientists build to learn. Engineers learn to build"