Why is light called an 'electromagnetic wave' if it's neither electric nor magnetic?
Light is an oscillating electric and magnetic field, so it is electrical and magnetic.
Later: re the edit to your question, I think there are two issues. Firstly the interaction with electric charge and secondly the interaction with magnets.
Light does not carry any charge itself, so it does not attract or repel charged particles like electrons. Instead light is an oscillating electric and magnetic field. If you take an electron and put it in a static electric field (e.g. around a Van de Graaff Generator) then the electron feels a force due to the field and will move. This happens when an electron interacts with a light wave, but because the light wave is an oscillating field the electron moves to and fro and there is no net motion. If you could watch an electron as light passes by you'd see it start oscillating to and fro, but it's net position wouldn't change.
This is exactly what happens in your TV aerial. The light (i.e. radio frequency EM) causes electrons in the TV aerial to oscillate and this oscillation generates an oscillating electric current. The voltage this generates is amplified by your TV. At the TV transmitter the same happens in reverse: an oscillating voltage is applied to the TV transmitter, the electrons oscillate in response and the oscillation generates an electromagnetic wave. So the process is oscillating electrons -> light -> oscillating electrons.
I'm not entirely sure what you mean by there is no transfer of electric charge/electrons (as there is in AC/DC current in space). If the above doesn't satisfactorily explain what's going on maybe you could expand on your question.
And finally on to the interaction with magnets.
The big difference between electric and magnetic fields is that (as far as we know) there are no isolated magnetic charges. If there were isolated magnetic charges e.g. if you could watch a magnetic monopole as a light wave passed by then you'd see similar behaviour to an electron. But there aren't, so you don't.
How can light be called electromagnetic if it doesn't appear to be electric nor magnetic??
But light does appear to be electric and magnetic in nature. For example:
Photovoltaic effect:
The photovoltaic effect is the creation of voltage or electric current in a material upon exposure to light.
Focus: Measuring the Magnetism of Light
Now two groups have independently demonstrated that a tiny, metallic probe will interact strongly with the magnetic field of light waves trapped in a sort of semiconductor “box.”
How can light be called electromagnetic if it doesn't appear to be electric nor magnetic?
According to the theory of Electricity and Magnetism, charged particles which are stationary are "electric", charged particles which move at a constant velocity are "magnetic", and charged particles which accelerates will emit "electro-magnetic radiation" which travels at the speed of light.
Charged particles can't interact instantaneously, but rather there is a field of energy which mediates their interaction. This field of energy is what we call "the electromagnetic field'.
In other words, "light" is the transportation of energy from one part of the electromagnetic field to another, and it facilitates the interaction between electric and magnetic objects, but is neither electric nor magnetic itself.