Most of the time when happening upon one of these threads, the OP will have an issue with coverage or speed or something like that. We will recommend using a wire because, even as a wireless expert who spends his days troubleshooting and configuring wireless networks, I will tell you that a wire beats everything. Many times, the OP will simply shoot down the idea without further consideration because they "just don't wanna deal with all that".
We are not telling you to use a wire because it's good for us. I'm telling you to use a wire because you are describing a VERY latency-sensitive application with strict packet loss requirements. Using a wire is the only way that you are going to be satisfied with the performance of that game given your stated situation. Period.
If you don't want to do that, that's fine. Not going to hurt our feelings.
But understand that given the situation you've presented us, wireless isn't the right tool for the job. Read the excellent word on Wi-Fi in my sig.