Consider the following premises. For all x_3, x_3 will play a game or x_3 is not a taxi driver. There is at least one x_3 for which if x_3 plays a game, then x_3 is a taxi driver. Can we infer the following from them? For all x_3, the fact that x_3 were a taxi driver does not imply that x_3 is playing a game.
That contradicts the premises. Therefore the answer is no.