Split view with green button does not work in macOS Sierra
Solution 1:
Go to System Settings -> Mission Control activate the checkbox displays have separate spaces.
Log out and In and check if it works.
Solution 2:
That is how it should work. It seems like something is interfering with the button press. Try disabling any window management apps such as BetterTouchTool. Also try using a first-party app such as Finder to make sure the app itself is not the one modifying the green button functionality.