Well, I should probably start by saying that there is a lot going on in this book, and at times that is to its detriment. 
 You won't find it anywhere on the promotional material, but The Galaxy Game is a loose sequel to Lord's previous work, The Best of All Possible Worlds. While it can be read on its own, some knowledge of Worlds will probably be helpful to the reader, as characters and themes reappear. 
 Now down to the nitty-gritty. 
 Things that I Liked: 
 I am so, so happy to see the results of events from The Best of all Possible Worlds. The continued realism of (view spoiler)[Delarua and Dllenach's happy, though not idyllic marriage contrasted with the disintegration of Freya and Lanuri's was a breath of fresh air. (hide spoiler)] Karen Lord is good at writing believable people and relationships. 
 In the same vein, I was pleased to see that the Sadira-on-Cygnus / New-Sadira / Cygnus-Beta politics -- which served primarily as backdrop in Worlds, are brought to the forefront. 
 Rafi Delarua's story is also interesting, if somewhat less-developed than I would have liked to see. His travels allow the reader to learn more about Ntshune society than the glimpses from the first book--Lord's worldbuilding ability truly shines. 
 Things that I didn't Like (or didn't like as much): 
 The story definitely gets off to a slow start--which, while not neccessarily bad, does make it a bit harder on the reader. 
 I'm still trying to figure out by Ntenman was given the privilege of 1st person perspective. Taking the Prologue/Epilogue into consideration, it might be a function of (view spoiler)[the devices to which Patron and Narua are listening (hide spoiler)], but that is unclear. 
 Similarly, Serendipity's purpose as a character is unclear. (view spoiler)[She doesn't play any particular role Rafi's escape, and while she provides a different perspective on event in Cygnus Beta, it really just amounts to one more PoV. Her involvement and pagecount are minimal enough that she could probably be cut from the book alltogether...unless she is to be important in a third book, in which case I'm disappointed she wasn't better utilized. (hide spoiler)] 
 The separate plots involving Rafi's journey and political events on Cygnus Beta don't mesh terribly well, although each is interesting in their own way. Part of this is because Rafi, as oblivious as he is, does not seem to be the ideal carrier of this story. He falls into events rather than instigating them, (view spoiler)[even when he seems to recognize his lack of agency, and even when Delarua lampshades his obliviousness (hide spoiler)], which makes it difficult to take him seriously. 
 Conclusion: 
 This isn't a bad book. The prose is wonderful, the themes intriguing, the writing style quiet and thoughtful--I did enjoy it. (of course, full disclosure, I would probably read anything by Karen Lord on principle; her prose is beautiful.) Karen Lord's exploration of culture clash, social change, and growing up all deserve attention. 
 In some ways, taking the bookend prologue/epilogue into account, this story felt like one long prologue, an interquel to define the changes between The Best of All Possible Worlds and whatever is next on Lord's list. If that is the case, I can't help but be disappointed. 
 However, structurally speaking, this book tries to do too much. I feel like it either needed to be longer to fully explore its plot and themes, or shorter to force those same plots and themes to come together more cohesively.