Consider this:
Wind is pushing a huge rock towards me at with massive force at 2m/s. I push against the rock at equal force so the rock stays still. I am clearly "working" very hard, using a lot of energy. However the distance the rock moves is 0m. Hence, work = distance * force. Therefore work = 0?
Why is this the case?
In the physics definition of "work done" energy is transferred from one object (the one doing the work) to another object or system.
When you push against the stationary stone you apply effort but the energy transfer is all internal to you own body - glucose being metabolized, etc.
You get tired but you do no work according to the definition above.
When you push something and it remains at rest your muscles transfer energy through isostatic muscle contraction/respiration. This means that even though the muscles don't move they convert the glucose into respiratory energy for muscle contraction that will be dissipated eventually by heating the surroundings. The only work done is that in contracting the muscle fibres, the rock needs to be displaced for any work to have been done on it.
In your case, no work is done.
Intuitively:
If you want to move a wall, you could push on it and you might use a lot of force. The wall isn't moving, and you are simply "wasting" your energy in your muscles. You are not doing any work of any value.
If you push a balloon you can push it far without any real effort. You might move it a long way but that required no significant strength - that is, no significant force - of you.
That is a way to understand the definition of work:
$$W=\int F \cdot \mathrm{d}x$$
Something has to move and it has to matter, or else we won't call it work nomatter for how long the air pushes on that rock.
As the wind pushes on the rock in your example, then if it cannot move it, actually no energy is wasted from the wind doing the pushing (friction, air compression etc. might still be relevant but not considered here). If a wall as in my examples is fixed to the floor and ceiling, then the floor and ceiling don't spend energy on fixing and holding the wall back while it is being pushed on.
That force is applied is not implying that energy is being spent.
(The human body is a special case since it requires energy of flexing muscle fibers etc. in the body to create a force. A human being is wasting energy while pushing but that is because of movements of stretching and compression within the body and has not got to do with the rock or wall that is being pushed)
By definition, work is the energy required by a force to displace something. So, you're not doing any work, you're just cancelling out the force being applied to you.
If you wouldn't push back then the other force would be doing work by displacing you. So, your work done basically cancelled out the work done by the other force.
