Can't move/snap Nautilus window to occupy left or right half of the 1366x768 screen - is it just me?

It would appear that this has something to do with the sidebar. My guess is it's a bug.

If you turn the sidebar off, the snap starts working as it should. Try the following commands from a terminal window.
Edit: The commands I've written out below hide and show the sidebar which can more easily be accomplished (as pointed out in comments) by simply pressing F9.

Turn the sidebar off:

gsettings set org.gnome.nautilus.window-state start-with-sidebar false

 

Turn the sidebar back on:

gsettings set org.gnome.nautilus.window-state start-with-sidebar true

 
While this is an answer, it's more of an option than a solution ... and probably not the solution you are looking for. It's certainly not the fix I or most other people would want, but it gives you a direction as far as reporting a bug!