Even if the doorposts are greatly out of alignment with each other, if a lintel connects them on their top, a mezuzah should be placed.[1][A]
However, if there is no lintel connecting them, and the ceiling merely flows from one room to the other,[B]
your playroom would be exempt from a mezuzah.[2]
[1] Da’as Kedoshim 287:3.
[2] Agur B’ohalecha 21:23.