This is a great thing you’re doing. Thank you very much for caring about others! It really goes to show your character and I appreciate it.
USO is a sort of official DOD program that provides recreation and relaxation for troops. They are a great resource. Every military base worldwide has a USO.Most airports do too, I cant confirm that every airport does but every airport I’ve been in does. When I was in service, I went to the USO about every month or so when in garrison for a road trip to different places. They do more than just “care packages”. Every base has a building for them. They have pingpong, video games, computers, books, and board games. And more. They also have trips. When I was in Florida, they actually took a group of us to Disney world for a two day trip (although I missed that one), and only cost us I think it was $25 for transportation (free hotel overnight and free park admission).
If that isnt your preferred route, there is also Toys for Tots, but keep in mind that is typically for quite younger children who will likely be unable to comprehend the complexity of this game.
Last option I can think of would be a library or other community organization that has a “board game day” or similar in their summer program.
If all else fails, you could always do a raffle on this forum where people sign up for only specific titles that they do not own and want to have a chance to win, and donate the proceeds somewhere. Just make sure the participants know where the donations are going beforehand, as not all donations are non-controversial.