If the author assumes that most people would even put considerable (probabilistic) trust into his assertion of having won, he would not maximize his influence on general opinion by employing this bluff of stating he has almost won. This is amplified by the fact that the statement of an actual AI win is more viral.
Lying is further discouraged by the risk that the other party will sing.
Agree that lying is discouraged by the risk that the other party will sing, but lying - especially in a way that isn't maximally beneficial - is encouraged by the prevalence of arguments that bad lies are unlikely. The game theory of bad lies seems like it could get pretty complicated.
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.