I read the article, and first, let me say that the invention is indeed a good one, but not one that will be widely adopted, except a way is found to make this invention decentralized and open source.
It has to be centralized and custodial otherwise it wouldn't be possible to use or set up. No private keys or seeds are involved because the receivers are not generating their own wallets. Anyone with a mobile phone and a valid SIM card can receive bitcoin without needing to set anything up the way we do. Download/buy/set up a wallet, generate a seed, back it up, send the person your receiving address, and finally receive the coins. All you need here is a phone number. The bitcoin aren't really moving over the blockchain, so it's account balance updates. But at one point in the future, something has to be recorded to the blockchain.
Technically it could be implemented in a
more decentralized way with a little more effort which would also solve the security problem.
For example the user's phone could send a message to the centralized server with the user's address to first fetch a list of UTXOs. Then the user can locally build a transaction spending any of the given outputs, even sign it offline (for example on another device) and then send it back to that server through SMS.
The first contact could also act as a registration so that the server can associate your phone number with your address so that if anybody wanted to send you coins they send a message to that server with your phone number and get your address.
The only limitation I can think of is the SMS size which user may need to send/receive multiple ones per tx considering the size of the transaction could be bigger.