Why wouldn't it?
The point of exercise is to simulate an environment where your body needs to adapt to survive it. For example, you don't need to run 30 km a day. If you consistently force yourself to do it, then over time your body will adapt to be strong enough to do it.
In your case, you actually do need to haul 245 papers in order to do your job. I'm sure you got pretty exhausted finishing it when you first started, but now it's probably significantly easier for you. That's exercise. You adapted. You become better at it. Eventually you start running to speed up your deliveries. Then your cardio improves even more.
Exercise doesn't have to fit in any traditional pool. The closest thing that comes to mind would be a loaded march or "rucking" with a sled pull (though sleds don't have wheels). If you're trying to assign it in an app or something, then you can also look up weighted walking/running with a backpack (as opposed to a weighted vest where the weight is more centralized in the body).