The pilot of the gyrocopter reported that during his approach to land on runway 31, the reported wind information indicated a gusting crosswind from the left. On final approach the gyrocopter required left stick and right rudder inputs to remain lined up with the runway. The pilot queried the air traffic control tower for the current wind conditions prior to landing, and was told 250° at 13 knots, gusting to 20 knots. The pilot intended to touch down with the left main landing gear wheel first, however, a wind gust pushed the gyrocopter to the right and the right main landing gear wheel “came down hard.” The pilot released the crosswind correction input and moved the control stick to the center, and the gyrocopter continued toward the right side of the runway. The gyrocopter subsequently exited the right side of the runway, rolled over and came to rest on its right side. The fuselage and main rotor driveshaft were substantially damaged. The pilot reported that there were no preaccident mechanical malfunctions or failures that would have precluded normal operation.