No, Software Engineers are not engineers on a technical level but they do the work of engineers[1] and the fact the industry has not caught up doesn't make what they do any less engineering.
[1] They are using math to solve real world problems that have billions of dollars and in many cases lives depending on them.
For one, I am sick of being called "not an engineer" when I bear more responsibility in dollars and livelihoods and use math more extensively in my job than most mechanical and electrical engineers I graduated with. In college I took all the same courses as the "real engineers"... I'm only a few credits shy of an Electrical Engineering degree. The "technician" majors took different courses. Less calculus, less physics, etc.
Heck, my stuff gets attacked by hackers on a daily basis. Show me something a civil engineer built where they need to worry about the level of security needed to protect against something like that. No one blames the civil engineer because they didn't explosion proof the road.
In fact a lot of the firmware I have seen Electrical Engineers write is terribly insecure and poorly written. Stuff a well trained Software Engineer would feel embarrassed about.
No, we are not legally engineers. But we should be.