I am pretty sure that "we don't want shopping malls to fall on our heads" count as a strong government and public interest.
Yes, I agree, but we're not talking about people misrepresenting their qualifications designing buildings, we're talking about people saying they're qualified to discuss timings for amber lights.
Restricting phrases like "I am an engineer" in the context of someone making final technical decisions concerning building design arguably makes sense, but it's no longer "narrow conditions" when you restrict such a vague, ambiguous, phrase under all circumstances.
I say arguably because if the conversation is something like:
Isaac: I say old bean, you're putting the wrong tensile cable on that suspension bridge of yours. Here, use this rope, should be strong enough
Isambard: Who the fuck are you? What is this crap?
Isaac: You can trust me. I'm an engineer!
Isambard: Oh OK. Hold a moment. There. Oh fuck, the bridge collapsed! I thought you said you're an engineer!
Isaac: I am. An IEEE certified software engineer! I know PHP! Whoopwhoop!
...then that law is obviously a waste of time anyway.