Rock climbing is fantastic, but as your claim that it doesn't make you 'fit' are a bit misleading. As with anything there are correct techniques and if overall 'fit'ness and being able to run a mile are related then you're doing it wrong in respect to your goal and you've probably chosen the wrong form of exercise.

Continuous bouldering again is a great way to work your cardiovascular while also stimulating your core. Slow top roping on the other hand won't be the same.

As seems to be the grandparents goal, you will definitely get a sixpack from rock climbing.