Where can I find a projector screen that 'dispenses' itself horizontally as opposed to vertically?

The screen I have seen used at meetings is on a track that can be pivoted to pull vertically or horizontally. Perhaps it’s an option as opposed to a standard use?

Gravity.

To expand on boxing’s answer… screens usually are vertical because it’s much easier to lower something and let it hang with gravity. Also with gravity, you’re guaranteed that your screen hangs vertically. If you have a horizontal screen, there would have to be tracks involved. If it’s automatic, the horizontal screen would have much more mechanics involved. I’d be willing to bet that any horizontal screen you find, you’ll have to pull out yourself.

Here’s one

Thank you thank you thank you!

much harder and more expensive to build, most will be attached to the wall with powered curtains or panels that open exposing the screen – this is what theaters use