IMO they are tracking ownership of each pair with the help of these tokens and once the real shoe is sold the token is transferred to someone else's digital wallet.
Putting a QR code on shoe is not really effective as it can copied/pasted on a different shoe etc.
what advantage does Nike gain for it being decentralized vs everything getting a QR code and you can verify with Nike that the person you are buying it from is the registered owner of said QR code.
Associating one QR code with one shoe is simply not the same thing. Nike doesn't have to make the whole ledger public through give the nature of blockchain, it can be assured that it has not been altered.
Also the thing is not stopping anyone from providing a wrong code. Unless every transaction concerning their shoes is recorded on the block chain, which it won't, and which brings privacy issues.
It's just shoes, no one will own or need to transfer 0.124 of those shoes.
If that’s the intention, it would be much simpler to just make a database and print a code on each shoe (probably already done to some extent). Therefore when a user wants to know if a shoe is real or counterfeit, they could use the code on a website to find out if it was the genuine article.
That seems like it would have far more uptake and use than a cryptographic model requiring wallets.