It is possible to scavenge the NFC antenna/chip from an Oyster card or indeed any other card, which the author alludes to in their video. There are details floating around on how to do it, by dissolving the card in acetone.
However, the relevant authorities might take a dim view of repurposing the transit card in this manner and probably have certain restrictions in place, to deter people from defacing their property. On another note, the author is using a NTAG213 on the watches sold via the shop and Oyster is Mifare, from what I can remember. There might be issues with response times regarding the proximity to the reader, if you wanted to experiment.
However, the relevant authorities might take a dim view of repurposing the transit card in this manner and probably have certain restrictions in place, to deter people from defacing their property. On another note, the author is using a NTAG213 on the watches sold via the shop and Oyster is Mifare, from what I can remember. There might be issues with response times regarding the proximity to the reader, if you wanted to experiment.