It is clear from the way that Tan presents the relationship between mother and daughter in this short story that the confrontation they have at the end is inevitable, and if it had not happened as indicated in the short story, it would have happened at some point, as Waverly becomes gradually more and more frustrated with her mother's involvement in her chess playing and the way she takes credit for her daughter's success. Note how this confrontation occurs when Waverly, recognising it was a mistake, but finding it impossible to stop herself, says: "Why do you have to use me to show off? If you want to show off, why don't you learn how to play chess?" These words clearly are insulting and are meant to wound her mother, and Waverly recognises that she has done something terrible the moment she has said them. The dream sequence in which the daughter and mother play each other at chess shows the outcome of this conflict and the way that her mother eventually triumphs, proving that Waverly's mother's will is very strong indeed and not to be trifled with.
Therefore, I believe that even if Waverly had not said those words, eventually there would have had to have been some sort of conflict between her and her mother. The dream sequence that symbolises this conflict could have happened at any time, and so could have been a suitable denouement later on. It is certain, however, that the conflict would have occurred one way or another, and the "opponent" with her "two angry black slits" would have gained victory. A different ending could therefore have focused on a different trigger to bring out the conflict, delaying it further. It is clear, however, that this conflict was bound to come out eventually.