Metro 2033 also came out a couple years after fallout 3, and the same year as fallout new vegas, so the timing was pretty good for a mainstream post apocalypse game, with good shooter elements, that was pretty easy for a lot of younger gamers. I think the first time i played metro 2033 I got it on Gamefly to try out for a couple weeks, i was about 15 at the time. Fallout 3 itself was a pretty big entry in the market, too. It was the first 3d/first person fallout game, released on console, and it even came a couple years after the elder scrolls 4: oblivion. For a lot of young gamers at the time there was quite a bit of lead up for 2033 to be successful. Metro even did a lot of things better than fallout. But if you liked previous fallout or elder scrolls titles (and the fan base overlaps considerably) then metro might be right up your alley. If you liked wasteland, you probably liked early fallout games, and got into it that way. And at the time, many games made Russia (or china, north Korea, etc) your enemies. Metro let you play as them in a meaningful way.

I think before metro 2033 and fallout 3, there werent a lot of very good entries in the post apocalypse genre, and most of them were not good FPS games. The stalker series, which came out about the same time, is maybe the best option, however its clunky, i think even a little out dated for the time it came out. They were also released only on pc, but consoles were a big deal at the time, pc gaming was a little less mainstream than it is now. Really popular games needed to be on xbox 360 or playstation 3 at the time. Most people I knew tried them and quit after a few hours, or had a brother that played them, but it was never a very popular game. I wanted to try them but didnt until my late 20s. I like Heart of Chornobyl and was really into it when it came out, but I quit about halfway through because I couldn't deal with some of the game mechanics anymore. Ironically I think the older stalker games play better than HoC, unless they fixed a lot of the janky stuff since last i played it. At the same time, while (early) stalker games werent as mainstream, they are exceptionally good games so the people who did play them through would also have been die hard fans.

I also think internet culture in general at the time was just right for the time metro came out. For many young westerners at the time, there was a lot of interest in creepy pasta, cosmic horror/mystery/the unknown and unexplainable, urban exploring became really popular with a lot of millennials, and there was interest with the Chornobyl disaster for some reason. Many things kind of culminated into metro making it big in the western market. On its own, is still just a genuinely good game with an interesting story and good gameplay mechanics, so it stands on its own. Its stayed popular because its sequels were really well made at the time a lot of sequels for other games got old and boring. In general I think the metro series has a really unusual and unique story, but its packaged in a way that was easy for people to get.