Taking an extreme example, it's possible to run faster if you use big spring type things (it may take some getting used to) but there are videos of people running stupidly fast with those "centaur" legs. Therefore the design/composition/mechanics of the shoe does have a significant effect.
There already exists a whole load of rules about the characteristics of acceptable shoes but they don't have anything yet about the amount of energy that can be returned, so that's where Nike have pushed things:-
From:
https://www.theguardian.com/sport/2018/jul/22/nike-shoes-vaporfly-sport (and
emphasis mine)
However last week, the New York Times, having analysed 495,000 marathon and half-marathon times since 2014 using data from Strava, reached a similar conclusion. Runners who wore Vaporflys, which have a controversial carbon-fibre plate in their soles, did indeed run 3-4% quicker on average than similar runners wearing other shoes, and around 1% faster than those using the next speediest shoe.
The International Association of Athletics Federations, the world governing body, also insists that Nike’s game-changing shoe meets all its requirements and “does not require any special inspection or approval”. Yet elite competition also requires a semblance of fairness. At some point the IAAF will have to rule on the permissible amount of energy return allowed from cushioning materials and whether carbon‑fibre devices in midsoles should be banned.
Nike are canny in this, they've probably got 3 or 4 more iterations of the shoe lined up with bigger and better returns but they know that going straight to the best design will have it thrown out or banned straight away. So they introduce the improvements slowly, just enough that the competitive advantage is there but not enough to people say it is too much. Competitors will catch up because they can get hold of Nike's shoes, take them apart, and copy the fundamental improvements, but Nike were first and have the hype and the sales that go with that. They can then choose to introduce the next improvement before the others work out what to do to improve on Nike's first iteration, etc.
See also swimming suits, trip suits for cycling, etc. Most sports are at it but most sports have stricter regulatory bodies and aren't dwarfed by massive sports companies with much bigger budgets.