I like to interpret this as Yukari severing the boundary between the player and the game--she cites the player's apparent involvement in multiple incidents (games), and presumably this is the player's first time going across the fourth wall into Gensokyo rather than just playing the games. She's breaking down the "boundary between reality [player's world] and fantasy [the world of Touhou]".
the whole pool is Touhou Lostword in a nutshell (?) (except the protag is a guy instead, and there is nothing like the Lost Word incident in this pool)
As a resident of Gensoukyou, I welcome you.Welcome to my gap.From here on... ...the place you stray into is the boundary between reality and fantasy.Starting from the "Red Mist Incident", there's the "Winter in Spring Incident", the "Eternal Night Incident", the "Great Barrier Incident", "Pandemonium", then "Mountain of Faith", "Scarlet Weather Rhapsody", "Subterranean Animism"... Through a variety of incidents and events, you've become involved with us. Or maybe it started even earlier...and I pray there will be more to come.