a few years back the MOI at my NROTC unit had been on American Gladiators back in the day. He had fought some chess pieces in his time in the Marines. I think he had been on the USMC rugby team when in a squadron.
That guy was friggin crazy. He was a -53 pilot and he was the kind of person who would not take no for an answer when he asked for something (like if he could be on All-Marine rugby). He was highly, highly narcissistic (think Alexander the Great) and he got out at 16 years(!) to go to med school at Morehouse. I wouldn't be surprised if he runs for President sometime in the next 25 years.
So yeah, there is a way to get to regularly play All-Service sports as an officer. You just gotta have the right combination of tact, panache, and machismo. Have fun with that.