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.
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.