Fundamental-ness of fundamental forces Example :
Consider a black hole and it's event horizon of radius R surrounding it . Suppose in the direction of a diameter of the black hole ( or event horizon) , there are two charged particles. Distance between these particles is 4R . In order for each particle to experience an electromagnetic force from another, a photon must travel between them as an information carrier. But in the midway, the photon will be captured by black hole. I conclude from this that the gravitational force of black hole affected the electromagnetic force between those two particles.
Question
Then why do we even call these forces as fundamental as if they are able to affect other forces by affecting their carrier particles? Had I wrongly interpret the meaning of fundamental ?
 A: 
Had I wrongly interpret the meaning of fundamental ?

For physics theories, yes you interpret wrongly.
The word "fundamental" in the way used in physics means

a : serving as a basis supporting existence or determining essential structure or function : basic

In the present mainstream mathematical physics theories, the basic theory from which all others emerge is the standard model of particle physics. It is the quantum field theory used for particles and is defined in dimensions of units compatible with h_bar , the Planck constant, where the model's calculations are validated. That is where the fundamental forces are defined as such: basic forces in nature.
All other theories can be shown mathematically to emerge from this underlying level,  thermodynamics, maxwell classical electricity and magnetism, .... Though the forces are fundamental because everything, at present, is supposed to emerge from these, the forces measured in larger dimensions are composite, and do not invalidate the word fundamental for the quantum field theory of the standard model.
For simplicity, let us take a different example of a sphere than your black hole. Take an apple, and two charged particles across it. The fundamental forces are interactions of the charged particle with the surface of the apple, not with each other as there is a multitude of charges shielding one particle from the other.
