I think it matters greatly whether the U. S. remains a superpower, especially since some other nations that might claim that rank -- such as Russia and China -- have not had especially attractive histories, especially in the twentieth century. The U. S. now has over 200 years of experience with democratic self-government, and, while we have certainly made mistakes, we do seem to have better track records than some of our potential competitors. I earnestly hope that both Russia and China will evolve in democratic directions in the future. If that happens, the world will be a better place for everyone.
Consider this - what is money? It's just paper and metal, really. Money only has value because people mutually agree that it does. One of the things that keeps US currency stable and maintains its value is our position in the world as a superpower. If people stop believing that the US has power, they will also stop believing in the value of US currency. If that happened, we would be at risk of a total economic collapse due to rapid and enormous inflation. Since many other country's currencies are indexed to ours, other countries would collapse with us. There would be chaos. If the money in your wallet and your bank accounts was suddenly only able to purchase half as much, what would you do?
It could matter to the rest of the world because the US has generally done a great deal to "keep the peace" around the world and to ensure things like secure shipping lanes so that trade can happen. The US has not been perfect, but it has generally tried to act to promote peace and to help other countries. If the US loses its superpower status, this situation may change. What will the next superpower do--how will it act? Or will there no longer be a superpower and will that make things more chaotic? So the US's status as a superpower (or not) will matter to some extent for the whole world.