It IS competition in one sense, as I mentioned... It is prime time TV for wrestling and WWE would ideally want that slot if they could get it. The only reason they probably haven't is the terms of their deal with Sky... When that expires it is doubtful they will re-sign for the lower amount Sky will offer... If WoS is established in that slot when that happens, it's competition for them.
No one is going to take WoS as a serious promotion... It'll be as before, a mix of the various promotions in the UK working together to make the show if it becomes regular.
The big thing WWE has done with their tourney is make talent sign deals which WWE can veto other appearances. They probably won't for the promotions themselves but they won't be going on WoS... they wouldn't do that if they didn't consider it competition in some way.