Please read the book.
The experimental line will be close to a lossless line. The theory for lossy lines has also been worked out. Just read and you will learn a lot!
You are openly displaying your own ignorance.
I took a looked at the pdf you linked and it seems he only considered the impedance and resistance of the circuit and not the energy storage capacity.
I do not think the ignorance is on my part. The results of my simulation using proper lumped elements perfectly matches the waveform shape that Derek obtained with his real world test.
The results show that the initial current through the lamp/resistor is due to transmission line capacitance charging so energy flowing through the lamp/resistor is due to resistor being in series with line capacitance (an energy storage device) being charged.
It is the equivalent of charging a capacitor from a voltage source through a lamp/resistor. So during the initial connection the current flows into capacitor (not through it) and that is what is seen in those first 65ns in Derek's experiment as well as in my spice simulation.
After that initial transient phase when at steady state the line will act as a purely resistive line so energy is transferred from the source to the lamp/resistor through the wires and current going in to the lamp/resistor equals current going out of the source.
Voltage across the resistor will be slightly lower due to energy loss on the transmission wires.
The main point Derek tried to make with both videos is that energy flows from source to load outside the wire is completely incorrect not only for DC but for AC/transient as well.
You can consider the lamp and transmission line one and the same so you can imagine a long filament 10m in both directions then you can understand that all energy provided by the source is dissipated in that filament in an uniform way when in DC steady state and a bit uniform during the initial transient due to capacitive and inductive characteristics of the line which is now also the lamp/resistor.