Comparing intelligence in animals is such a hard thing to do when we barely understand it in ourselves. As they say in the article, we frequently consider dolphins more intelligent because they are more sociable and exhibit similar characteristics to us.

An easy (although not necessarily correct) way to define intelligence could just be the ability to learn, although even this can be hard to define. Some animals can learn fast, while others have a larger space in their memory. As was pointed out, dogs are able to learn significantly more words and more complex phrasing than other animals, but at the same time they have been conditioned for a very very long time to understand human voices, dolphins much less so.

Dolphins are in a completely different environment, which results in completely different conditioning. Perhaps the reason they seem similar to us is because they are in a similar place in their environment. They're fairly independent species, not relying too heavily on other species, or being heavily preyed on by other animals. This could allow their brains to evolve in a similar way to ours, which aligns with our definition of intelligence.