Apple Watch Not Allowed to be Activated by New Owner
You can easily ask Apple's servers if a piece of hardware is currently locked:


https://www.icloud.com/activationlock/


On e procedural side, https://support.apple.com/en-us/HT205009 covers the unlocking process, but the seller needs to log into iCloud.com and delete that watch from their account.  

They use the settings web app and "Under My Devices, click the Apple Watch that was sold and then click the X"

Should take them 5 minutes or less on a computer to sort that out.