In order to end the game by domination you need to own every player’s original capital.
If it’s getting close to the turn limit (usually 500 on standard speed) then you may be in a position to win by score as well, because you conquered several other empires.
i will say this: in the late game, you have several tools available that make world conquest go very fast. One of them is Fascism, which is extremely strong with +5 strength to all units, and 50% more production.
The main ace up your sleeve is Bombers- bombers can rip an enemy city to pieces, letting you stroll in with a tank to take the bombed out, 1HP city.
Because domination requires capital cities and only capital cities, you can also use nuclear weapons to simply blast a path through their civ, decimate their capital, and send in a quick unit like a tank or helicopter to snatch it in one hit. Nukes can raze (completely delete) non original capital cities!
Be warned: the fallout will also hurt your units, which is why it is recommended you use a high movement unit to clean up after a nuclear strike- otherwise it will take too long to march and die from the radiation.
If you have gathering storm, Giant Death Robots also make very quick work of enemy empires.