I can imagine people having fun getting lost in the flow of playing a competitive sport. I've also heard some people experience a post-workout high. But does anyone actually feel pleasure in the moment while lifting weights, jogging, cycling, etc?
If so... what does it feel like? Is there anything the rest of us can do to cultivate such a mindset?
Of course you can be pushing hard or some jackass in a car just passed you with inches to spare, and those times aren't fun, but most of the time it's fun. My wife says I do my best thinking while I'm riding. If I'm on a group ride, there's often good conversation with friends.
Depending on where you live, it might be nice to see a lot more of what's around you on a bike. It's similar to OP's idea of getting lost in the flow of a competitive sport. You get lost looking at all the places that pass you by. You can take random routes each time and learn the city around you pretty well. It doesn't hurt to have your headphones in and listen to an audiobook while you're doing this either.
I never really got into running because it's so much slower than biking. You will see a fraction of what you see on a bike, so I think it probably gets boring quicker. Plus it puts more strain on your joints.