No, this industry is far from being like the other engineering disciplines. It should be like them, but it is still far too immature to be put at that level.
Licensing would require settling on actually understanding that software development is an engineering activity and not an extended CS 401/501 project. The industry isn't even mature enough to consider licensing either.
In Australia, non-citizens can get engineering licenses. The process is basically the same as a citizen (just more complicated because of visa requirements, as you would expect).
What? Of course non-citizens can get an engineering license. It can be trickier if your education is from outside the US, but citizenship is not an issue.
Our starting salaries are much larger than other engineering disciplines, and I'd argue we don't make nearly as stable constructions as other engineers. In Australia the starting-out civil engineering salary is almost half the starting-out software engineering salary (and this is a country which hates technical innovation and prefers building more mines).
We shouldn't make as stable constructions as other engineers, for very good reasons: they're building things out of concrete, iron, and steel that are meant to last for years doing a very predictable job without alteration after their initial construction. If you don't get it 100% right before you close up a building, it's going to cost millions to go back and fix it.
As programmers, conversely, we build text files that are expected to change every day as the business needs shift, and we know up front that most of the code that we write will not survive as-is. Speed of iteration is far more important than getting things right the first time, and the cost of a delay in the name of building something right can be much higher than the cost of refactoring the simplest solution that can possibly work once you actually need to (YAGNI is not something you'll hear very often in physical engineering fields).
The other engineers do their part, and then software controls it. Bad software destroys things. People get killed by accident.
Then there are the security holes in things that will never get updates, the malware-infested webcams and TVs... this too impacts the world.
We can combine it all: connected cars. This isn't "other engineers". It's software developers -- call them programmers or software engineers if you like.