Unfortunately, all Experience Manager settings are only modifiable by a user with System Administration rights. This is purely a UI trick, as the CM core itself will not enforce this rule.
The decision was taken to do it like this during XPM development due to added complexity of adding one more right to Tridion and investment in training, etc. Experience Manager is already complicated enough to set up, adding one more security layer would not make it simpler. The downside of it is that in secure Tridion environments you probably need to open a ticket to get someone to click on that checkbox.
We are currently investigating changing this so that it is a bit more user-friendly and requiring less Admin intervention, but it will probably not come soon enough for you. The only alternatives you have right now go through creating a custom extension that would set the same values (this information is stored in the page's Application Data) and Experience Manager would pick it up from there. Or, if it would make it easier, you could create a custom page instead and give users some sort of page list with check-boxes to turn the selected pages into page types or something along those lines.