She wasn't in uniform and in her own time, what's it got to do with the boss?
As the article points out public drunkenness is quite taboo in a conservative Muslim society such as Qatar. Employees work visas as dependent upon sponsorship by their employer, so if she was arrested or something it could come back to them. Even if nothing illegal was done it would still damage the reputation of the company.
Public shaming like this is an unfair response though, it should be been a private conversation with her and a general memo to staff without mentioning names or specifics.