It does seem like hes playing, My friends amazon did a similar thing but instead of being upsidedown she would hang from the top by her beak, spread out her wings a bit and grab her feet together and shake them up and down.
Though I do know with amazons if they fluff up, spread their tail and pin their eyes its a sign of agression, or just a warning to stay back, dont touch me. But yours seems more like playing, sonce they can pin their eyes when they want.
Gotta Love your Birdy Babies <3
Buster, Gracie (Rip[tumor]), Willie, & Hector (RIP[Sharpie and unconcerned vets..).