I assume that you are seeing the "Block" and "Priority" options from the screenshot, but not the "Sensitive" one. In this case, I have been able to replicate your situation.
In the Sound & notification settings page, there is an option called "When device is locked". If this is set to "Show all notification content" then the "sensitive" option is available. If it is set to "Hide sensitive notification content" then it is not.
From a little bit of experimentation, I think that this option is poorly named. As far as I can make out, what actually happens is,
- If it is set to "Show all notification content" then the content of notifications is shown on the lock screen unless you have specified that that app's notifications are sensitive, in which case they are hidden.
- If it is set to "Hide sensitive notification content" then it is assumed that all apps are sensitive, and no notification contents are shown (but the titles still are).
- If it is set to "Don't show notifications at all" then no notifications are shown on the lock screen.
In other words, despite the wording, the "When device is locked" menu is an overall setting, and it can be overridden for individual apps when this is applicable.