Zigbee is great for communication instead of WiFi, but it’s just one part of the equation - it says nothing about the specific commands a device will respond to. You couldn’t pair a Philips remote with an IKEA lightbulb.
Matter attempts to fix it by actually defining the protocol that these devices use. It’s also fully local and open source, which is great. The actual transport layer can be WiFi, but it can also be Thread, which is a newer standard based off Zigbee, and AFAIK some Zigbee controllers can be reprogrammed to support it.
They don’t specify what transport layer they are using here, but considering the kind of devices they are showing (battery-powered remotes) it’s almost definitely Thread.