Genre fare often offers implicit commentary on the state of social affairs (sometimes it's explicit). This can be illuminating when you are familiar with the social context, but I feel I am missing something when I watch films from other countries. So I know that Train to Busan is seen by some as an allegory for Korean politics, but I don't know enough about the topic to be able to identify the allegory. It's not that the allegory is missing, it's that I am missing the allegory.
Which thus leaves me to react to Train to Busan on its genre elements. And on that level, this is a terrific movie. Wikipedia calls it a "zombie apocalypse action thriller", and that pretty much gets it. The zombies are of the fast-moving variety. One article by Ezra Klein suggests that such zombies are "too fast to be truly scary", and a case can be made that the slower version of zombies have a better chance of taking over the world. But the fast ones are indeed scary in the immediate sense, especially when there are lots of them. This was the case in World War Z, but the huge budget for that movie seemed to make it more a special-effects extravaganza than a character-driven thriller.
Train to Busan is constructed like a classic thriller. Right from the start, there are intimations of the horrors to come, but they are only intimations. Still, the suspense is serious (after all, we know the zombies are coming). And once the zombies arrive (fairly quickly), the suspense is replaced with open-jawed thrills.
Two things in particular make Train to Busan impressive. First, there is a dedication to the characters, who are painted in quick scenes but who always feel slightly more than stock from the genre's closet. We care about the characters, which isn't a necessary component to a zombie thriller, but it does lift this movie a bit above the rest. Second, the zombies really are impressive. It's not just that they are fast, it's that they feel real. I don't know how much, if any, CGI Yeon used, but it's very old-school in its presentation, as if instead of going straight to the computer, they actually hired a bunch of extras. Yeon's previous work was in animation, and the zombies have the kind of physics-defying qualities you'll see in cartoons.
The tension is mostly non-stop, with little time to take a breath. I don't suppose Train to Busan will appeal to people who don't like zombie movies, but it certainly ranks high within the genre.