Modern exercise is structured and accessorized.

Paleolithic exercise is organic and creative.

Modern exercise is based on sustaining heart rates and numbers of reps.

Paleolithic exercise is about listening to your body and responding to it in kind.

Modern exercise is 30-60 minutes on the treadmill 3-5x/week and getting on hyper-isolatory weight machines.

Paleolithic exercise is about moving around more, sprinting like your life depends on it every once in a while, and picking up heavy things the way humans actually pick up heavy things, with their whole body.

Exercising in modern times is almost always a manufactured activity designed to achieve some health benefits, rather than some naturally occurring activity that stimulates your body. In this sense there would be no such thing as "Paleo Exercise", only activities that might have been common in Paleolithic times.

Since you have to make up an exercise routine if you want to add simulated activity into your life, you can use your imagination (or that of other people) to devise movements that might have been common, and presumably we have adapted for. Or you can imagine that some shortened artificial set of moves captures the essence of, or even optimizes, the healthful component of activity. In this case, you wouldn't necessarily be re-enacting.

It's not clear to me that paleo-style exercise has a clear advantage, although it is certainly plausible that modern exercise theorists have missed some important components of movement that are good for us, and it is likely there are styles of modern exercise that are even hurting us.

For me, there's no such thing as paleo exercise. Our ancestors did physical activity for a reason - hunting, build shelter, playing, fighting, etc. So their bodies adapted to what they needed, what we now call functional fitness. Our required physical output today is quite low, as we outsource most of the mentioned activities to third parties and machines. So we now 'exercise', which plays no fundamental role other than...to exercise. I think functional training is great. Perhaps you won't get quite as perfect a body as a scientific bodybuilder, but you'll be able to use it - many modern athletes fail the functional test. We all know a long distance runner who's insanely weak, a gym rat who is so big they walk funny, etc