To reiterate the question posed by A Game of You: what is a woman? This question echoes in a multitude of ways throughout this arc of The Sandman. We see it in the various ways that Wanda is judged not to be woman enough--how she's drawn, how others perceive her, the shape of her own nightmares, how her family chooses to remember her after her death. We have it in Barbie's neighbors, who struggle to maintain their identities as they attempt to rescue her--Hazel and Foxglove must cope with managing their identities as lesbians as they also deal with an unexpected pregnancy, Thessaly must drive herself with thoughts of revenge to continually reconstruct her self-identity as someone powerful and not to be trifled with. And of course the question defines Barbie's quest in the Dreaming--it turns out she is not there to save the land she has dreamed of (it is inevitably destroyed in the end as part of a compact that cannot be mitigated), but is instead there to find out who she is and what she can be. A Game of You is literally the "game" of figuring out who You are, but it's a game with ferociously high stakes when you're a woman.
The villain of the arc, the Cuckoo, is not an external threat. She is instead a part of Barbie's identity, a malicious refashioning of the inner child. The Cuckoo is a remnant of Barbie's rich childhood fantasy world, but she is a particularly feminine remainder of the imagination. We're told by the Cuckoo that there are differences between the fantasy worlds created by boys and girls: boys dream of themselves as empowered heroes, while girls dream of familial belonging and domestic happiness. Although we might wish to disbelieve this way of defining imagination according to a gendered binary--it comes to us, after all, from a seemingly insane villain--the surrounding fictive world of the comic goes some length to reify that idea. It is Wanda (never woman enough) who reads superhero comics; Barbie, on the other hand, has a terrible experience when she goes into a comic shop because she is too obviously a woman in a space that caters to products for and by the male imagination. (And damn, that scene is one solid punch Gaiman aims at the jaw of mouth-breathing comic guys. FATALITY.)
Of course, this leaves us with some room to postulate that the gendering of imagination is wholly culturally-constructed, but I'm not convinced that A Game of You really hammers that nail into the coffin. If this arc is about Barbie's search for an authentic self in the wake of her divorce, she plays an amazingly passive role in the resolution of it; it's Morpheus (absent for the majority of the arc) who swoops in to make the big changes. Barbie earns a boon from Morpheus for her role in fulfilling the compact, but she spends it on protecting her new "family" of neighbors--reaffirming that her imagination is still defined by domesticity and belonging. And though there is a sense of Barbie honoring Wanda as a woman by painting over the birth name etched on a tombstone that forcibly re-inscribes her as essentially male, it's worth noting that the lipstick Barbie uses to write "Wanda" over "Alvin" is temporary--it will wash off, and the name cut into the cold stone will surely outlast it.
What is a woman?
It seems like we still don't know.