Dynamic Ragdoll

The models use layered animations. The run_loser is just a layer for the upper body pose, while the legs will be hooked into the player's actual movements. Props don't support layered animations as far as I've seen, so I don't think you can do it.

and for the record this isn't ragdoll. ragdoll specifically means NOT explicitly animated, and just free to fall as physics dictates (such as corpses).

I just remembered something I was working on a few years ago that might actually do it for you. The point_posecontroller entity allows you to control certain animations in certain ways, it I had used it for making a prop_dynamic playermodel walk.

Took me awhile to find which VMF had it all buried within, but I think I found everything you'll need.
Make a point_posecontroller and set the Prop Name to the name of your prop_dynamic. Set Pose Parameter Name to move_x (this is the forward/backward movement axis). Pose Parameter Value will be how fast you want it to animate, from 0 (stopped) to 1 (full speed). Keep in mind this isn't just a framerate adjustment, it actually links into the model animation stuff and it will animate correctly just as if a player was moving at that speed (walk, run, etc).

By the way, that ring in your first screenshot looks carved. Don't ever do that. Use the arch tool.