Is Arabic Language a sine qua non skill if you want be a successful professional in the PR field in UAE? What about other languages?

I think it really depends on which company you're applying for and your tasks/missions. 

For some PR positions, if you have to deal with press from the Middle-East, or writing/editing tools, I guess this is mandatory. 

Otherwise English and maybe another language might be sufficient but I would love to hear from other people on this question.