The video is not clear on what is happening. A single photon travelling in vacuum can never create a real electron positron pair, because of inconsistency in the rest frames of before and after. Before there is only the photon which has no rest frame and 0 invariant mass. After there is an electron positron pair whose added fourvectors will have at least 2*m_electron invariant mass.
This is what is happening as far as quantum mechanical solutions go for creation by an incoming impinging photon an electron positron pair.:
The incoming real photon exchanges a virtual electron which interacts with a virtual photon with the electric field of the nucleus, andthe incoming energy is converted to the outgoing pair of a real electron and a real positron. Thus energy and momentum balances are kept.
what is exactly the electron(matter) part and the positron(anti-matter) part in the electromagnetic wave? is't the oscillation or is't the E&M fields or is't something entirely else?
There does exist the phenomenon of virtual electron positron feynman loops as the photon goes along in vacuum, but they are a mathematical construct that allows calculations of finer structure than the first order calculations ( the above diagram) give. And that is another story that needs quantum electrodynamics to understand the mathematics.