A game like an FPS doesn't need much speed (they can work with modem-level bitrate). They instead depend on having low latency, or ping time. Since the moon is so far away, it takes a signal 1.3 seconds to travel to or from it.
One speed interferes with multi-player twitch FPS here, and it's not the bandwidth - it's the speed of light. Try playing an FPS with 2+ seconds of lag and it'll be very, very unpleasant.