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.