I'm uncertain on bringing those lost options in GUI back other than to recommend clearing data of Settings app from Settings → Apps → All apps → Settings → Clear data. Reboot and see what happens. In the event of failure, you can consider factory-reset.
That said, if you're simply concerned with changing Window/Transition animation scale and/or Animator duration scale, then you can use
content tool which do not require root access. You can refer to Christopher Galpin's method for an approach requiring root access.
(Solution tested on Android 4.2.1, 4.4.2, 5.0.2 and 5.1.1.)
Setup adb in PC and execute
adb shell settings get system window_animation_scale # for Window animation scale. Some ROMs have this key under global table instead of system. So replace system if command gives null
adb shell content query --uri content://settings/system --where 'name="window_animation_scale"' # an alternative to above command. Make replacements as appropriate
If the first and the second command returns you a decimal and a string beginning with
Row:, then you're on the right track. Now do
adb shell settings put system window_animation_scale VALUE # Replace VALUE with a decimal, such as 0.75 or 2.0. The minimum and maximum I've seen are 0.0 and 10.0
adb shell content update --uri content://settings/system --bind value:s:VALUE --where 'name="window_animation_scale"' # an alternative to above command. Make replacements as appropriate
In order to change Transition animation scale, replace
transition_animation_scale. For Animator duration scale, replace with