Three claims are being made by the conference:
1. Dolphins are as smart as humans.
2. Therefore, they should be counted as people.
3. Therefore, we should afford them the same rights as other people.
Number 1 isn't backed up by much evidence. The journal article linked on this page says that dolphins can understand simple but grammatically novel instructions from their trainers. Admittedly, that is rather impressive for an animal, but parrots can also do that, as can computer programs. That's not enough to justify saying that dolphins are as smart as humans, let alone that they should be thought of as people.
Number 2 is also out. Even if we assume, despite the lack of evidence, that dolphins are as smary as any human, that's not enough to call them people. As crudely as rarborman put it, being able to do things that a person can do does not a person make: There is no parity between a person and a dolphin. The dolphin cannot teach a person to communicate with it, holds no power over any human and makes no attempt to reform its behavior based on moral concerns.
Even Number 3 is unsupported. Male dolphins gang-rape female dolphins in order to reproduce. They murder infants born to other dolphins and kill porpoises for no known reason. If we provisionally assume that dolphin are as smart as people and that dolphins should qualify as people, the correct and moral response would be to immediately imprison the entire population until such time as we can communicate with them and introduce the sort of social contract and justice system that keeps humans from acting like complete monsters. Because if they actually are people, and you're not using that as a backformed justification for why they should be protected (as I suspect the conference is), than dolphins should be the world's biggest 'human'-rights violation to date.