I am impressed that you have received the dreaded regrets, and that it has barely slowed your stride. That is a good sign of commitment from my perspective. One of the pearls of wisdom I can take from this is that if an initial denial stops the plan in its tracks, then the CGA likely made the correct decision. It seems reasonable to presume there will likely be larger emotional and mental obstacles at the academy, and as a commissioned officer, than what this day presents. If this day is enough to make an applicant quit, then perhaps that is one part of the system doing its job, and both parties will dodge an uncomfortable union. That thought brings me some peace on an otherwise somber evening.
I have read numerous times here that it is next to impossible to say how much this or that matters, as the admissions staff is looking to create a "class". My advice here is worth what you paid for it, but I would say involvement in a group, preferably showing and obtaining leadership within that group, is more important than what that group is specifically doing, within reason. I would think (having admittedly never been behind the curtain) that it need not necessarily be a sport as long as your PFE shows you are well prepared for the CGA. Given that it will be your second time around I think spending the next 6 months beating that PFE into submission can speak to your athleticism. Sports bring organized group efforts, often under stress. They typically require cooperation and sacrifice. I think demonstrations of teamwork, perseverance, and commitment should definitely be shown in some regard, but that sports unto themselves are not the only way to demonstrate those skills and experiences. In that context, given that the school exists to shape and sharpen leaders, whatever role you can playing in leading as opposed to following will reflect well on your next application, but you may be competing against 2 of my daughters, so forget I said all that. Soda, donuts and naps for you, bub!