How does the magnetic field of an inductor affect the operation of a DC circuit?
Unfortunately, your source does not have a good understanding of physics, so has chosen some bad analogies. 'Inertia of electron flow' is harking back to the water flowing through pipes analogy, which is OK for voltage, current and resistors, but gets stretched too far when it comes to inductors.

Current flowing in the wires of an inductor create a magnetic field in the inductor core, which is at right angles to the wire.

Energy is stored in the magnetic core of the inductor. This energy has come from the power supply's energy source. Energy is stored as the magnetic field, and has nothing to do with kinetic energy. It's stored in the field, just as an electric field stores energy between two conductors at different voltages. What the field is is best left to quantum physics. You can think of a field as stretchy rubber sheet if you like. It isn't, but it helps some people.

It's this stored energy that drives the 'unusual' behaviour of capacitors and inductors. Capacitors store energy as the square of the voltage. Inductors store energy as the square of the current. If you try to change their voltage or current (respectively), you have to change the stored energy. If you try to do this quickly, then it requires (or generates) a high power (energy change per time). If you've ever short-circuited a big capacitor, or open-circuited a big inductor, you'll know what a spark you get. 

There are two limits to how much current can usefully be pushed into an inductor, but neither has to do with the magnetic field interacting with the wires. 

The first is heat. The current generates heat in the resistance of the wire, and the first thing to fail as the temperature rises is usually the wire insulation. So as long as it's limited to a very short time, very large currents can be applied, before the temperature rises too far.

The second is magnetic saturation. At a certain current, the core reaches its maximum field, and its permeability drops. Higher current (up to the thermal limit) will not damage the inductor, but its inductance value will have dropped radically, and little more energy can be stored. It's the practical limit for operation. If the inductance value is being relied on to limit a changing current, onset of saturation is a bad thing and usually results in a further sudden increase of current.