I suspect it's very hard to enforce. We can legitimately argue.
1) We are a far bigger, more successful club than other of the above. Have won more leagues than both combined.
2) In WEST hams case they have moved to an athletics tracks synonymous with the Olympics, they dont own the stadium and any corporate partner would fear it is associated with the Olympics. Spurs are building a stadium that is at the same site as before, so it's not new in the same way.
3) Our location is state of the art, theirs is not.
4) They are not the first clubs in their city. Indeed they are not in the top two most successful in their city.
I could go on. However it would be hard to argue any of the above. It is only logical we could attract higher sponsorship than them.