Again, that was the Vanilla rule - "the last civ to never have lost their original capital wins the game by domination."
The BNW changed the victory condition to, "One player needs to control all capitals." However, there's apparently some fine print - while playing an unmodded BNW game, I controlled all capitals except for one which was controlled by a CS. This triggered domination victory.
They are not the same:
"the last civ to never have lost their original capital wins the game by domination"
vs
"the rule to win domination is: no other major player should be in control of
ANY original capital cities"
What I said is more or less the negation of the negation of "One player needs to control all capitals", so it should be the same. Of course this is without including city states, which would make sense considering the experience you had.
What would be interesting to know is what would happen if a CS takes the last capital, so let's say you have one capital left to conquer and a CS ally snipes it from you, would that trigger a DomV for you? I will test this out with IGE and get back with the results.
L.E. Tested this with IGE on a tiny map with 3 civs:
1st scenario: An ally city state conquers one capital, the next turn I conquer the other capital, but right before that I declare war on my CS ally. I got the Domination, so it doesn't matter if the cs controlling the last capital is your ally or not
2nd scenario: I conquer one capital, and leave the other capital with 0HP and an ally CS infantry next to it. I declare war on the CS, just to see what happens (apparently the CS is still at war with the last AI). On the CS turn it conquers the last capital, and this triggers the Domination screes, so you don't even have to be on your on turn to win domination.