I do think the cleanest and most fascinating interpretation is what the title says "One life, drawn at random from all who have ever lived" which clearly is about random people and has nothing to do with the year.

But I think experientially, the preferred feeling for a user is a random deep dive into the circumstantiality of different eras and different geographies than our own, rather than a true-to-life re-rolling that would constantly turn up 20th and 21st century outcomes. So the spirit of it is probably closer to the random year idea, but it's literally not random year, but maybe randomly something else, like eras however designated.

I’ve reflected in the past about how lucky I am to have been born where I was, when I was, and be given the abilities that I have. Sure there are plenty of people that were luckier, but also a lot who were less lucky, most of whom are dead.