Is this theory relevant or not?
The Michelson Morley experiment destroyed the concept of the classical luminiferous aether.
But if not, how it could happen that something is interacting with something other without any transmission media
At the micro level nature is quantum mechanical. The classical electromagnetic wave is a confluence of innumerable photons, the elementary particle of the electromagnetic interactions. These photons propagate with velocity c and are also fundamental in the interactions at the microscopic level.
Quantum field theory postulates fields for each particle that fill up all space on which creation and annihilation operators generate the interacting particles. The difference with the luminiferous aether is that quantum fields are Lorenz invariant .
As pointed out by BobBee in the comments, one has to be careful in the use of the word "medium". Medium in physics needs an extra attribution,. The attribution by Maxwell had the adjective "luminiferous", light carrying medium, i.e. a substance or material in which something exists or grows or through which something can move or otherwise travel. The experiment showed that this substance did not exist. The quantum field theoretical model which applies for light propagation also describes how interactions at a distance happen, by the transmission of energy and momentum packages moving with a maximum velocity of c .
When you throw a ball and hit somebody, it is action at a distance without a medium, that is a rough analogy of what is happening at the quantum mechanical level of interactions, (rough because there are integrals involved)