It appears that Ubuntu Mate 14.04 users the Marco window manager. The man page tells me
Marco configuration can be found via the main MATE menus, under
"System->Preferences->Windows" and "System->Preferences->Keyboard
Shortcuts" or by running the commands mate-window-properties and mate-
keybinding-properties respectively. Advanced configuration can also be
achieved directly, via dconf-editor under "/org/mate/marco/".
I have looked in both places and see that "[X] Enable side by side tiling" is selected in Window Preferences and also in dconf-editor.
I am told in dconf-editor
If enabled, dropping windows on screen edges maximizes them vertically and resizes them horizontally to cover half of the available area. Drag-dropping to the top maximizes the window.
I observer the following behavior... If I open my home folder and smash the window against the left side of the screen it does in fact expand to full height and half the width of the screen and it resides against the right side of the screen. If I open another "Place" and do the same thing it again is sized to half screen. However, if I try to move one of the windows to the right side of the screen - sort of the whole reason for "side-by-side-tiling" in my mind - the window assumes its original size. If I smash a window into the right side of the screen I observe that nothing happens.
How do I make two windows share the screen equally - side-by-side?