Touhou is a a vertical, top-down shooter, or in my words:
"Proof that hell exists."
Touhou is popular because of a wide variety of elements such as the music, characters, gameplay and difficulty
( Personally, I love it for everything ;3 ).
Here's an example of all 4 of those elements 8D
[link] (btw, don't be put off on the difficulty of that stage, that level is that hardest onein the 7th game O:
).