Papi (and later Suu) are playing what appears to be a Nintendo Wii.
The character in the game look like a hermit crab, this is a reference to Okayado's icon character the "hermit crab".
Kimihito breaks the fourth wall when he sees Cerea's sword: commenting "I haven't seen this in a while. Since chapter 4, I think?". However, in the english translation, Kimihito instead comments on how she hasn't been this "ranty" since chapter 4.
When Centorea identifies Suu as a Slime, Kimihito asks if it is like the Dragon Quest mascot.