Are fundamental forces, forces or net forces?

The electrostatic force or the electric field (force per unit of charge) is the force the charges feel. It's not the net force of many forces, since it's the only force.

A force field is a function from the space variables (points in space) which returns the force (in the form of a vector) at that point. The other points in space, where the charge isn't, aren't feeling any "force", nor those "forces" aren't having any effect in the charge. The field is just a construction for representing the (net, if there is more than 1 charge) electric force at each point.

The force between two point charges IS defined as a single force acting along the line joining them , but that between two distributions of point charges or one distribution and one point charge is a Net force according to the superposition principle. Because we can not break the smallest force between two point charges to a sum of other elementary forces , since we already assumed that it is a point charge and that its dimensions are very small, at least in theory. I hope I answered your question.

Thinking about it again, your interpretation is actually a little interesting as an intuitive explanatory picture. It is a (not often discussed, as far as I know) corollary of the shell theorem that results when you combine it with Newton's laws, particularly the third law.

Newton's third law says that every force has an equal reaction force. Thus, when we integrate over a spherically symmetric shell as in the shell theorem, we can similarly be integrating over this reaction force (i.e. the force on that point of the shell due to the external charge). We're able to translate these reaction forces to the center of the sphere, because:

1. Each force has partner on the other side of the axis that connects the sphere's center to the external particle, so we can translate these forces to that axis without changing the torque on the rigid spherical body.
2. Once the forces are on the central axis, and cancel with their partner, it is clear they do not torque the axis of symmetry, so we can translate them across the axis to the center of the sphere.

These forces will add in superposition, and the result, by Newton's third law, is that the force on the shell equals the Coulombic force imparted on the external charge, but in the opposite direction, exactly as if the shell were a point charge located at the center.

The important thing is that the shell isn't made to spin, or anything. (Although that is a simple consequence of $\nabla\times\mathbf{E}=0$.)

Once you add a bunch of external charges outside, this simple view still holds in superposition.

So this shows that you can think about the classical electrostatic force as a net force, as long as that force acts on a spherically symmetric charge distribution with the same total charge as the point charge, and all external charges are outside the radius of that ball.

Intuitive Explanation

Let's look back at your picture, and the above connects with an intuitive picture of the field lines.

First, you blow up the point charge to a finite size (as discussed above), so you can see the difference in electric field line densities across its surface. (Although it's not too important, note that inside, the field will appear as how things would be if the point charge was not there in the first place.)

Because each field line starts at a positive charge, and ends at a negative charge, we can imagine each field line as a "tug" on the charged particle. (For negative charges, the tug on it is in the opposite direction as the arrow on field line.)

For a charge in free space those field lines go out to infinity, and they are tugged equally in all directions. (Hence, not at all.)

When a positive and a negative charge approach each other, the field lines deflect toward one another, and the net tug on each particle is attractive.

When charges of equal sign approach each other, the field lines deflect away from each other, and the net tug on each particle is repulsive.

As long as you still draw the electric field lines such that they follow Maxwell's equations (i.e. get the divergence right, have no curl), I am fairly confident this intuitive picture should hold in the electrostatic case for point charges.

I still think it's easier just to stick to the Coulombic force, but your idea can lead to a nice picture, as I've tried to (non-rigorously) show.

(Note: I cleaned up this answer in an edit, adding the "proof sketch" at the beginning.)