I'm not suggesting your opinions are wrong, of course, but I had a much different impression. Obviously Player of Games is well regarded by many people, so I'm curious to know what I missed.
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My general impression was that the Empire of Azad was that its conception lacked imagination. The peculiarities of the species (the three sexes, the society built around a board game, etc) could have made for a very interesting culture, but those instead the peculiarities were mostly left untouched and the culture was recognizable as human in every way. The greatest offense, in my opinion, is that the most interesting part of the book (the game Azad) was left almost entirely undescribed. An alien species should be different. Vastly different. These were humans painted green on Star Trek.