It seems like that's a different variant. "In addition to the paper circuitry, PulpaTronics also applied another of these experimental technologies...", so the "geometric pattern in the antenna" thing is a different tech from the "paper circuitry" thing.
EDIT: https://www.jamesdysonaward.org/en-US/2023/project/pulpatron...
From this other article it sounds like there is no other variant, this is indeed just encoding in the antenna shape. In which case using the terms "RFID" and even "paper circuitry" are big stretches...
The geometric pattern appears to be a red herring. In the article one of the founders says "but it doesn't need to be scanned visually" (so it's not like a barcode).
In the Dyson page (nice find), the last slide shows the electrical response compared to a metal tag, using a vector network analyser, and includes the text "Over 1000 readings, our paper-based tag performed equally well as the copper tag".. which suggests it's intended to work with current readers.
The way I understood this is they developed the concentric ring pattern first, build a prototype using standard copper etching, and showed that it worked. Then they showed they could achieve similar results by fabricating the same pattern using a laser and paper.
Which means you need new readers. Readers that essentially are pretty fancy network analyzers.
If they want to use current readers, they need a tag with logic gates, one that can send a digital response.
EDIT: https://www.jamesdysonaward.org/en-US/2023/project/pulpatron... From this other article it sounds like there is no other variant, this is indeed just encoding in the antenna shape. In which case using the terms "RFID" and even "paper circuitry" are big stretches...