just as useless in practical terms
That's not "exclusive". The "pixel" is the exclusive bit.
However, as written it sounds like you are essentially objecting that an address along Central Park (in New York city) is "not exclusive" because there are other "Central Park"s in the USA.
They numbered all the pixels in the CCD of the telescope's sensors. The WFI is a 300.8-megapixel camera. So each pixel in that array is numbered. Wherever the telescope looks, your pixel will sense some light or darkness. That's it. That's the Tweet.
No coordinates involved. In fact, you'll need some math to convert the ordinal numbers of the pixels back into a 2D coordinate on the plane of the sensor array. It's laid out in a unique way. You can see the layout in the official logo.