It's not that you need to play the games in order to understand the plot, but they are pretty cavalier about spoiling things that happened in earlier games, the assumption being you should already know what happened.
Curious Village, Diabolical Box and Unwound Future sort of form their own little trilogy this way. It's not like the stories are connected, but the later games will spoil some things from the earlier games.
Last Specter, Eternal Diva (the movie), and Mask of Miracle are sort of the same way to each other, but they don't make many references to the other trilogy that much (mostly because they're prequels).
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Okay, I rolled a 14. What's that mean? Hsu
That you're a cheater. This is a 12-sided die. Chan