As already pointed out by @Marius Ladergard Meyer 6 a force doesn’t need to do work to cause acceleration. Another example is the static friction force by the ground acting forward on a car wheel causing the car to accelerate. The energy comes from the fuel not the ground.
What’s more if the person and the skater are the system then the reaction force of the ground and railing is an external force accelerating the COM of the person and skater.
On the other hand if you include the Earth in the system the forces are internal and the acceleration of the COM of the system is zero.
Hope this helps.