Guy uses a Raspberry Pi acting as a Wi-Fi router on his home network, running a custom DNS server that looks for IP addresses associated with push notifications, and redirects the DNS requests to nonsense IP addresses.
That’s the blocking part. So far, so good: now, in order to pick up notifications, you need to put it into the mailbox. Inside the mailbox is a mechanical switch that closes when the phone is inserted. The switch is connected to a Feather S3 board, from Unexpected Maker, that tells the Raspberry Pi to stop the monkey business with DNS. The Wi-Fi network reboots and, when the phone looks again for the Google servers, all the previously blocked notifications come through. Congratulations: you are now in charge of your phone, rather than the other way around.