Unfortunately, not at present. We would love to set this up but our charity does not have the money needed to do that. It is on our 'wish-list; hopefully someday. For the moment, you would need to add the distances you clock up using your Apple Watch manually to World Walking.
Once you have connected your Apple Health Kit with World Walking, the way the World Walking HealthKit/pedometer works is if you open the app frequently (at least once a week) World Walking uses the iPhone’s pedometer data (rather than the specific HealthKit data) which can be different. For example, if you go for a run with an Apple Watch and don’t take your phone, the phone’s pedometer wouldn’t count that but HealthKit would.
The reason we decided to on this approach is because the pedometer data is always up to date (you can walk 10 steps then query the pedometer and it’ll show those new 10 steps), but with HealthKit data there is sometimes delayed (you can walk 10 steps and query HealthKit but it might not show it for a few minutes or more as it collates data from different sources “intelligently”).
If we had the funds to create an Apple Watch app and we wanted the distance shown on the watch to match what’s synced with World Walking, we could use HealthKit. This might mean that although your steps would not always sync immediately, it would catch the instances where people are using Apple Watches or adding steps directly to HealthKit.
I hope this explanation helps. Sorry we cannot do more at the moment.