I struggled to find much information, but this post suggests that supporting vertically written languages in form inputs is rare. It also suggests that there’s little support for it.
Well, I’m a Japanese and the traditional Japanese texts has been written vertically for so many years like yours (BTW, what language is it?).
It’s true that you see many vertically aligned Japanese letters on the web, but they are image files, not texts. Virtually all the body texts are written horizontally. As for inputs, no one expects vertical ones. I’ve never seen them. It’s not supported in the current HTML.
Probably you will need to develop a custom input plug-in for browsers, maybe using Flash or ActiveX … I really don’t know.
So, I encourage you to persuade your customer to forget it.