As far as I can tell, the offence here is that he used privileged information (contact details from her job application) to contact her about a personal matter (the date).
Once her application was rejected there ceased to be a meaningful power relationship. Some people seem to be implying that there remains a professional power relationship since she may choose to apply at the company in the future, but I doubt that has any practical or legal teeth. The same could be true of all her potential future employers OR her future employees, vendors, customers, etc...
So what he did was creepy and unprofessional, yes. But let's understand why and to exactly what degree before deciding what the appropriate response should be.
Personally, I would contact the HR department and inform them that I didn't appreciate company employees using the contact details from my application to solicit me for a date.