I wonder if Phoenix Wright is considered an adventure game. I am really quite unfamiliar with the adventure game genre so I am trying to get a rough idea of it. 

I haven't played this game, but from my research it appears to be an adventure game, yes. I would say that if a game similar to this one is entered into this jam, it would certainly qualify.

alright, thank you for your quick response.

I always considered adventure one giant map like Metroid or Goonies II. Before MetroidVanias became popular it was GoonTroid.

It seems like you're thinking of "action-adventure" games, honestly. While the genre names are confusingly similar, the "action-adventure" game genre and "adventure" game genres are completely unrelated. action-adventure games are like Legend of Zelda, Metroid, Tomb Raider, etc. Adventure games are like King's Quest, Grim Fandango, Blackwell Legacy, etc.