While the timeline of Touhou Project contains many events, there are two important eras for when it comes to running a game: the Modern, and the Old.
Old Gensokyo is the simplest. It covers the time before the introduction of Dueling, and does not use those rules. Fights are much more similar to in normal D&D; monsters will kill players and terrorize humans, and humans, typically the players, have to stop them. For those who wish to feature named characters, consider them as having found a way to reform themselves by the time they are slated to turn up in the computer games, or that this is simply a story that may or may not be true.
Additionally, a story may be set even earlier, before the forming of the Hakurei Barrier in 1885. Since this barrier is what separates Gensokyo from the Outside World, stories set before its forming can take place when Youkai, Gods and the like still roamed much of the Earth.
Modern Gensokyo is set after the introduction of Dueling. It uses both the Dueling Rules and Pichuun!, and the order of things has been altered greatly to prevent death. This can either make for a much more relaxing game, or it can cause the focus to shift from combat to diplomacy. Of course, most Youkai will refuse to acknowledge any conditions without a fight, so it's still important to know how to beat people up.
Before a game starts, be sure that the players are aware of the rules of the game. Healers, for example, may lose much of their value if PCs are unlikely to die. Then again, their use during a fight itself may still be invaluable. Either way, make sure players are aware of the rules so that they don't end up playing a character who feels useless due to the way the game works.
Note that there are still Youkai outside of Gensokyo, so a story could potentially take place in the Outside World, where modern humans no longer believe in fantasy.