No, it's nowhere near as high tech as the article makes it sound. In contrast to how it works in the UK for example, in Saudi Arabia you have to go through passport control whenever you leave the country. This new system checks if the person leaving is a child or a woman and texts their father's or husband's phone number if they have it registered. They can find that information because it's all part of the ID system that's been implemented for decades.
Sounds like the couple that got the text wasn't even aware of the service to begin with.