Can someone elaborate on value proposition for this sort of device? What problem(s) does it solve?
A digital blood pressure monitor effectively does the same thing, but without the need for a trained professional. It still has the cuff and the pump. To measure the blood pressure it has to pump and cut off the blood flow to some extent. This obviously makes it inconvenient - it's uncomfortable, it's fairly large, you have to put it around your arm (or wrist or finger), and the pump is usually noisy. The new device seems to be an improvement in these categories.
The main improvement here is size though. Blood pressure monitors usually go around your upper arm and the machine that houses the pump and the electronics is even larger than the cuff. This makes taking frequent measurements difficult. There are smaller devices that go on your wrist, but their accuracy tends to not be great. Even the standard digital blood pressure monitors suffer from inaccuracy.
If the device in the article does what it says and is actually close to as accurate as a regular digital blood pressure monitor, then hopefully we will get more blood pressure data on more people. This should hopefully allow doctors to figure out better treatment plans. However, I find it unlikely that it will match the accuracy of the commonly used digital blood pressure monitors.