I think you should define 'energy' somewhat. As it stands, both you and the person you and wanderr are right as far as I'm concerned. My body is pretty tired right now and even hurts a bit after 2 hours of bmx. But yes, I still feel energy, the urge do the things, to be creative and whatnot. But that's mainly mentally. I couldnt really go for another ride. Tomorrow though it'll be different: after a night of good sleep I'll be energetic both physically and mentally. An effect which unfortunately wears off after some days. Likely the reason sports are addictive.

Also it's really not as simple as 'play, don't exercise'. I do admit the playful sports work better for me, but it's not that the more boring plain exercise ones don't do anything at all. And I can imagine some people just don't care for the play at all.

Another aspect: something like 'plain' road cycling is fairly easy on your body and is not really hard to do. The 3 other sports you mention are different though so they're just nor for everyone. As much as I love jumping a set of stairs for instance, the impact is hard on your body and the older I get the more care I have to take. E.g. if I don't properly warm up now I'd just damage myself. That used to be different when I was 20. And it's extremely likely at one point I'll just have to give up on bmx because I simply won't be able to do it anymore. Man, I wish that day would never come. But it will.