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.
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.
Yes, many births would be within the last 200 years but it’s still very different to be a man born in the year 1950 in New York vs a woman in 1950 in rural China.
It's clear to me that an even bigger HC crowd would howl "Oh, how boring, look at him choosing pretty much only still alive people" if he had done the 'uniformly random" selection. C'mon!
And IMO, a website that's 95% stats by volume very clearly is about stats. If the goal is teaching anything, it's teaching stats. It literally does animations showing the random process, and explicitly says how likely each outcome is, even sorts by likelihood in some places.
Again, I wouldn't have as much of a problem with that if the website itself didn't explicitly say that recent births are more likely than non-recent births.
Personally, the one 1990s person I've got was far more interesting than the dozen of 5th-15th century children that all died of one sickness or another before the age of 2. If anything, it's the dying of dysentery that should be non-uniformly random.
The skew towards the present isn't as stark as that. World population has exploded in the past couple of centuries, but it hasn't been high for very long. 1900 to present only covers ~11% of all births.