If you mean dominant in terms of having the largest population: Fertility and longevity are closely related in most animals - we can compare different species within the same genus and see a relationship between number of offspring and health/longevity. Producing offspring is very energy-intensive and stressful on the body, leading to shorter lifespans. This should be easily incorporated into building a fantasy setting with elves so long-lived that they rarely have offspring, and total fertility may not be any greater than replacement (total number of offspring over the life of the female may only be 2, with rare examples of third children). Long lives make their population seem extensive as so many generations are alive at once, but in terms of total fertility they are barely replacing their losses.

If you mean in terms of technological/political domination: As Max Planck once said - science advances one funeral at a time. Long lives allows elves to get stuck in their ways - fixed in their views, beliefs, and methods - even when the world moves on. They simply cannot adapt to changing circumstances due to harboring old prejudices, clinging to the outdated understandings they grew up with, not adapting to shifting landscapes (geographic or political), or merely failure to incorporate new methodologies. This leaves them like a picturesque ancient rural village - sure it is pretty, and a restful place to retire to, but no significant economic activity is taking place. Every elven village is like this being exactly the same as it was a thousand years ago... including the residents. Some well-traveled outsides may know of them as quaint places to visit, but they have no meaningful impact on the world.

If you mean dominant in terms of having the largest population: Fertility and longevity are closely related in most animals - we can compare different species within the same genus and see a relationship between number of offspring and health/longevity. Producing offspring is very energy-intensive and stressful on the body, leading to shorter lifespans. This should be easily incorporated into building a fantasy setting with elves so long-lived that they rarely have offspring, and total fertility may not be any greater than replacement (total number of offspring over the life of the female may only be 2, with rare examples of third children). Long lives make their population seem extensive as so many generations are alive at once, but in terms of total fertility they are barely replacing their losses.

If you mean in terms of technological/political domination: As Max Planck once said - science advances one funeral at a time. Long lives allows elves to get stuck in their ways - fixed in their views, beliefs, and methods - even when the world moves on. They simply cannot adapt to changing circumstances due to harboring old prejudices, clinging to the outdated understandings they grew up with, not adapting to shifting landscapes (geographic or political), or merely failure to incorporate new methodologies. This leaves them like a picturesque ancient rural village - sure it is pretty, and a restful place to retire to, but no significant economic activity is taking place. Every elven village is like this being exactly the same as it was a thousand years ago... including the residents. Some well-traveled outsiders may know of them as quaint places to visit, but they have no meaningful impact on the world.