Glad you asked!

Most importantly, the game in 1933 showed that the "through ticket to Manila" version of War Plan Orange would not work. The capital ships would arrive there with underwater damage and no way to repair it. They'd have to go back to Pearl Harbor, or the west coast, to reach facilities that would allow repairs. In which case, what was the point?

After that part, US war plans in the Pacific involved island hopping, so forward bases could be obtained where repairs could be performed. This had a number of important downstream implications: amphibious assault against protected islands would be necessary, with the equipment, training, and doctrine that implies (these would go on to be applied in the various invasions in Europe, including D-Day). Mobile dry docks would be needed (the US led the world in these in WW2, including modular ones that could be hooked together to produce something that could service a battleship.)

The need to fight across the Pacific implied ships would be up against land based planes in the Mandates (various island groups assigned to Japan after WW1). This meant carrier planes had to be on par with land based planes. The British did not learn this lesson and started the war with greatly inferior carrier planes (some of which were biplanes!)

The games illustrated that carrier operations needed to be optimized for rapid recovery of planes. The more rapidly planes could be recovered, the more planes a carrier could launch (and then recover before they ran out of fuel.) Capt. Reeves went on to command USS Ranger, where he pushed strongly to accelerate flight operations, eventually developing the system of landing planes before a wire crash barrier, then pushing them forward of the barrier to rest on the deck as more planes landed. This avoided the need to cycle the elevator(s) during landing operations. The US Navy was the only navy doing this at the start of the war. Fueling and reloading, even storing, aircraft on the flight deck was a natural extension of this. As a result, US carriers could carry more aircraft than those of other navies; they were not constrained by the size of the hangar.

The games showed that carriers were vulnerable to damage to their flight decks from even small bombs, and that there would be great value in the context of a campaign if this damage could be repaired by the ship's crew. This led the US to designs where the flight deck was unarmored, made of wood on a steel framework. USS Enterprise could not have participated in many of the carrier battles of the war (and the US would have lacked any carrier at the final climactic battle off Guadalcanal) had this not been the case. The British, in comparison, had armored flight decks, which meant after any damage to them they needed to go to a repair facility.

The circular formation used in carrier task groups in the war was developed in the games.

The games showed there would be great attrition of aircraft and aircrews. This meant the fleet had to be backed up by a very large pilot training program, as it was. The Japanese never understood this implication (at least, until it was too late) and failed to implement a scalable pilot training program, nor adequate pilot recovery efforts, and suffered from catastrophic decline in effectiveness as their first team pilots were lost.

The games showed the importance of scouting. Various ways of doing this were tried, eventually leading to investment in flying boats (which also were imagined as bombers, although they were overshadowed in that respect.)