Matter itself is not a network transportation protocol . The usual allegory is that if you’re sending a letter, matter controls the format of the form that goes inside the envelope. But something else actually schedules the trucks and delivers the letter.
For matter, at the time of this posting, it can be matter over Wi-Fi, matter over thread, or matter over bridge.
For this particular device, it’s matter over Wi-Fi, so you must indeed have it connected to your Wi-Fi before you’ll be able to complete adding it as a matter device to any platform.
See the IPv6 specification in the product description? That has to do with Wi-Fi.
That said, most matter over Wi-Fi devices are designed like many other home automation devices these days so that they initially get onboarded to your SmartThings app via Bluetooth and then creating the Wi-Fi connection is A step in the matter process. So some of this is just terminology, and some of it is details of the onboarding process, but this particular table lamp will definitely need to be connected to the same Wi-Fi that the SmartThings hub is connected to as part of adding it to SmartThings.
FAQ: What do I need to add a Matter device to the SmartThings app? Do I need a bridge router device?