False, in South Africa you have to pre-register to vote at a precinct with a photo ID, then on election day you have to show your photo ID to vote at the place you pre-registered for. After you've voted they mark your thumb with the ink as a secondary (or tertiary) security measure.
I'm honestly not going to check every country on the list, but it's blatantly false in South Africa where I've voted before. And I'm going to bet it's false for a lot of other countries on that list too, like India.
[1] https://en.wikipedia.org/wiki/Election_ink