^reasonably sure the joke is 1st-place kid has just been getting shoulder rides from her totally not adoptive mother (strictly speaking a wyvern but anyways), who as it happens is also totally not the old-salt ex of booba eyes owl lady in second place (who is also kid #1 de facto adoptive mother and current guardian)...
As for the rest, well, look up the tags Saria x Silence
, Hoshiguma x Ch'en
and Franka x Liskarm
- strictly speaking the relevant partners are wyverns and a lung (Chinese dragon) which are in-universe distinct races from dragons, but let's ignore that for the sake of the gag now.
... but Franka, having an ounce of shame? impostor amogus