Okay, first of all : I kinda botched one of Kiriya's line last week. Sorry about that. Was about to change it at the last minute, but that didn't make the final cut.
On the other hand, though, for that one Poppy's line on episode 6, I still believe that she's talking about the genre (rhythm games in general) instead of the game (Doremifa Beat) as her favorite. The way she's wording it, it is true that you can interpret it both ways as Japanese is ambiguous in general, but the wording feels too specific if she's implying that she's talking about the game, not the genre, and it feels like the sentence and the one before it is an explanation of the genre for the little kids watching at home who might not know what a rhythm game is.
Yes, I'm well aware she's the mascot, and if any, I feel she would've worded the sentence differently if she wanted to talk about the game, not the genre, especially because she's the mascot.