Earlier quoted context omitted.
They don't: there are different UIs for different screen sizes. Your data is in the cloud (eg a Word Document in OneDrive on on Azure) and you can access it from a full desktop program on a PC or Mac, from an app on iOS or Android, or via a web browser on any device that has one. This is a cross-platform vision that works both online and offline (unlike Google) and that ultimately doesn't care which device you use (u…
But that's not the vision from the article ("Microsoft is about to turn a phone into a real PC") or this thread. Take a phone and plug in a bigger display and keyboard and mouse and suddenly it's a desktop computer. So a single application is going to need to cope with a 4" touchscreen display with no keyboard or mouse as well as a multi-monitor setup without touch, but with a keyboard and mouse.
Yes, it reflows. You use the app when it's in phone mode, and you get the full desktop-style UI when in Continuum mode. There are several demos online. See for example, from April 2015 (so it's surprising you haven't seen it before):
Windows 10 Continuum for Phones LIVE DEMO https://www.youtube.com/watch?v=Sc1efHpPIVo
More recently:
Enhanced Continuum For Phones demo (Build 2016) https://www.youtube.com/watch?v=tv5Y9vNOSMc