Dragging a dialog between screens with touch does not allow you to drag a window from one monitor to the other as part of the window disappears when you lift your finger to bridge the gap between the two monitors:

This is actually a limitation of macOS. Windows can only exist on one display at a time, and in order to change which display that is, they have to be dragged while the cursor jumps from one monitor to the other.

This of course makes it basically impossible to move windows between monitors using only a touch screen, since by their nature it's not possible to drag items from one to the other with a single gesture!

One way to work around this is to open System Preferences > Mission Control and uncheck "Displays have separate spaces". When that's turned off windows can appear on more than one monitor, so moving a window between displays with touches becomes possible. Turning that off has other effects though, so this might not be a suitable solution.