That seems like a strawman. The complaint is that he described himself as a professional engineer while his license had expired. As in, during that period, he wasn't a licensed engineer, and therefore shouldn't have called himself one.
The complaint is that, in his advocacy, he described himself as a professional engineer, which he obviously is. The idea that one needs to stay in the good graces of the state in order to reference one's experience in their field as part of their political advocacy cannot possibly withstand genuine first amendment scrutiny, can it?
Being licensed isn't to be within the good graces of the state, it's to prove the licensee has the requite knowledge and experience to design and construct things which, when fail, people die. This is something we want in society.
First, I don't agree that licensure accomplishes this.
But second, it sounds like you agree with the plaintiff here. Nobody is asserting that he had a legal right to perform civil engineering after his license lapsed. What he's arguing is that he had a right to reference his experience in civil engineering as part of his political advocacy.