Alt-Tabbing through windows I'm used to having Alt-Tab set to cycle forward through the windows of a single app and Shift-Alt-Tab to go backwards. I had this working on Yosemite by fiddling with the shortcuts in System Settings > Keyboard > Shortcuts.

But after upgrading to El Capitan, it is only Finder that responds to these commands, no other Apps, although they have not assigned this shortcut for something else.

Is there a way to enable this behaviour on El Capitan for all apps?
I am not sure I understand your problem. The functionality is there and works as expected. Go to System Preferences / Keyboard / Shortcuts / Keyboard and choose whatever key combination you want for switching windows in Move focus to next window setting, say Alt+Tab. This will switch application windows forward and Shift+Alt+Tab will switch application windows in reverse order, which is exactly what you wanted. The reverse order functionality is already implied by the Shift key and you don't need to set it separately. Mind you that if you choose combination that already includes the Shift key for forward order it will not imply the shortcut for reverse order without the Shift key.