You already know what tools you're going to be using, so I'll do other concepts then.
What is defenitely essential would be:
Health for the ragdoll.
A realistic health thing gives somebody the satisfaction of killing the ragdoll in one blow. However, the health should be relatively as high as a human's "health" would be. A sharp hit in the head can knock the ragdoll unconscious, while crushing or stabbing it would be an instant kill.
Being able to break the bones of a ragdoll would be great fun, and still simple. Say that if you broke the leg of a ragdoll, you would simply remove the constraints of the swinging of that leg, and let it turn 180 degrees instead of 90 degrees.
Breaking the ribs of the ragdoll could make it go completely limp due to the pain, but leave it alive still.
Another essential thing: Breakable structures.
Things like timers or the ability to break walls is both essential and great fun. While you could use timers to break a joint holding a hammer, keeping it from swinging till you want it to, you also get a "whoa thats so cool" feeling for being able to smash the ragdoll through a wall and such. It also expands the options of things you can do. If a ragdoll flies through the support of a building, the building would fall on the ragdoll and crush it.
Ropes:
It would be a useful tool. Stretchers, doors, guillotines, levers, etc.
Big essential thing: The ragdoll shouldn't be limp.
You already have that done. A standing ragdoll is much more fun and playable than a ragdoll that lies lifeless on the ground.
(In my opinion) Essential/fun thing: Being able to impale the stickman, and possibly the walls.
Impaling the stickman would be great for the tools of arrows and javelins or shrapnel from an explosion sticking into the ragdoll. It would also give people a great feeling by impaling a ragdoll into the wall. I played a game once where that was possible, and I spent most of the time just trying to do that, instead of following the game's storyline.
(Mostly fun) needed thing: Explosions
It doesn't have to be an explosion, but something that presses force against anything within its "blast radius." It would make throwing things at intense speeds possible, along with shooting the ragdoll from a cannon into whatever trap you have.
(More essential to the funness of the game) Dismemberment.
Being able to use guillotines on the ragdoll, being able to tear off their arms with stretchers, having shrapnel from an explosion rip apart the ragdoll, the list goes on. It would be fun.
Back to the actually essential things: Backgrounds.
It would be incredibly annoying to have to build supports for a building that reaches the top of the screen. If there could be a "cliff" or a large section of the ground sticking up that would make building high towers much easier.
A "depth" function.
So you could build things in front of structures that are already built. And be able to keep hammers and heavy flying objects and the like from damaging your towers.
A play/pause function.
So you can build towers without worrying about them falling over halfway through.
Points:
To count how much damage you've done to the ragdoll. Get an extra 5000 points for breaking bones below your neck, and 15000 points for breaking the head. Same amount of points for dismembering the bodyparts or the head.
Is this enough?