You can store private keys on NFC tags. You can store a private key on anything that can hold text, including paper.
Only thing is, from scanning through that page, it looks like thats an NFC reader and not an NFC tag.
RFIDs hold just numbers / data, such as a public key.
NFC is like RFID but 2-way (hence the C for Communication), which can be used for signing a message with a private key and sending the response back.