In America, people often state their race is black, or African American. Yet Africa is an entire continent, with more ethnic groups, cultures, languages and religions than possibly any other, barring possibly Asia.
Yet I don't think anyone would be able to say with a straight face that Malcolm X, Martin Luther King and Muhammad Ali aren't the same race. Despite them tracing their heritage back to many different cultures and nations, as well as their own personal differing culture, religious and spiritual differences.
This is why race always has to work on a much higher level than nationality or ethnic group. "Hispanic" covers an entire continent and a half of nationalities and groups. "European" similarly spans not only Europe, but many parts of northern Asia as well (not to mention the more ubiquitous "white" that includes many North Americans and Australians).
The case that there are thousands of races is impossible to even make, aside from the most hardcore eugenics proponents. At best, there are a dozen or so. And the only real way to track this, especially as groups blur and migrate, is phenotypical much more often than cultural.
Regardless, Orlesian is a nationality, not a race. Leliana was born in Ferelden, of Ferelden parents. Yet she was raised in Orlais and became the token Orlesian in the DA:O group, the prototypical representation of that nation. She was Orlesian, regardless of her "race."