Solution: Miss Peregrine's Home for Peculiar Children
Written by Ethan
Right off the bat, it seems like Miss Peregrine has made an illegal move, as PITCH seems to have no way to link to the BASE which has already been played. However, looking at your response to her play, as well as the flavor text of "stacked", it turns out PITCH can be a valid play if you "stack" the letter C on top of the B, making CASE (similar to how the game Upwords is played). This is confirmed by "an instance?" (the definition) as well as "if that's the case". This process continues, turning PITCH into PATCH ("cloth to mend"), PLAYER into PLAYED ("took part of this game"), etc. Each stacked letter is always part of the previous played word. Taking the letters that got changed in each round (the letters under) spells BIRDS OF METAL.
One note is that I wrote this before Huntinality's Piles of Letters puzzle. Though both are technically Upwords, I think this puzzle's mechanics are different
enough to call it a different puzzle.
One thing I aimed for were clues/responses that were ambiguous until both you understood the mechanic and fit the general flow of the conversation. I think I implemented this relatively well ("if that's the case" and "I was skeptical you would win"). Some responses were rewritten from feedback by DaroCaro, thanks!