OK, before reading the wall of text I'm about to post about a seemingly simple topic, understand that I am kind of a nut about axe/maul work. This is not necessarily because I'm generally a nut, but rather because my work has given me occasion to spend extended periods of time splitting wood and chopping roots. As a result I've devoted an above average amount of thought and study to how generate the maximum amount of power and efficiency in this movement. I've done so out of the general intellectual curiosity which I try to apply to everything but also out of the more immediate and practical desire to accomplish the greatest amount of work with the smallest amount of pain.
When I swing an axe/maul I initiate the movement by laying the handle across both my thighs parallel to the ground and dropping my hips/flexing my knees into about a quarter depth squat, body weight over my heels. I then forcibly extend my hips, glutes, knees bouncing the handle off my thighs to rapidly accelerating my mass upward and the maul overhead. As the hips drive up and the glutes pop, the spine lengthens allowing the rib cage to move away from the pelvis, and my weight comes forward and up onto the balls of my feet permitting a nice, long, fluid upswing finishing in a very tall, fully extended overhead position.
Like I said, I find the basic movement pattern to be pretty similar to a kettlebell swing, a hang clean (or maybe a hang or whip snatch), a vertical leap or a football hit for that matter. It is a hip-dominant, multi-joint, full body movement. This is also, I believe, what Dan John is describing when he talks about explosive "hip hinge" as it pertains to O-lifts, K-bell swings and athletics in general.
It's "hip snap/glute pop" that is the engine for the whole movement. Your arms and shoulders are essentially along for the ride while providing direction and stability. Your grip stays light until the top of the movement when you need to tighten up to stop the swing.
The load is light (6-8lbs for a maul) but the acceleration is very rapid so you need to generate a fair amount of force. At the top of the swing you need to forcibly tighten your lats, brace your abs and shorten you hip flexors to first arrest the upward momentum at the top of the up swing and then reverse it to drive your body weight down into your down swing. As your hands approach your waist/groin level you sit back onto your heels and break at the hips and stick your ass out a little again to accommodate the swing (so you don't axe handle yourself in the junk) and so you can engage your glutes to brake the swing (if necessary) and reset for the next one.
Again, your grip stays light and your arms relaxed until the instant of impact when everything tightens up to brace for impact and maximum power transfer. This all happens very quickly (again very rapid braking and subsequent acceleration) and thus requires you to generate a fair amount of force, especially if you need to swing really hard.
It may not be a "leg work out" per se, however given the likely number of reps performed and the speeds generated, I would say it's more on par with k-bell or light and fast med ball work or even erging on a rowing machine (although rowing is more quad-dominant) than it is with bench press as a full body exercise. I've split large quantities of hard wood before and I can tell you from my experience that afterwards, I had some pretty bad DOMS in my hips, glutes, core and lats and some lingering fatigue in my quads. My hands were beaten, bruised and bloody from the repeated impacts but my arms and shoulders were fresh as a daisy.
I didn't take any metabolic measurements, but I was a hungry, tired dude for days after and when I did that type of thing more frequently and ate less (but still shitloads of) food I got seriously, alarmingly lean. I am confident that I could hurt some pretty young, fit guys pretty badly if I took them out to do this for an afternoon at a moderate (but stiff) pace or a much shorter "workout" at higher intensity. Anecdotal, I know, but that's my experience FWIW.