The video is almost right, but fails to explain the capacitor across the points. It doesn't just "absorb back emf", it allows the circuit to oscillate with the inductance of the transformer.
Without the capacitor the voltage from the coil, when the points opened would try instantly, in a few billionths of second, to rise to 1000 or more volts, this would cause the points, still only slightly opened to arc over.
With the capacitor, the coil's inductive flyback current must charge the capacitor to a high voltage at a much slower rate(over some fraction of a millisecond), so by the time the voltage is high enough to arc, the points have already moved too far apart for the voltage to jump that new point gap distance. The result, instead of creating an instantaneous arc that will just arc across the point contacts and kill all the spark coil energy, you get a lower voltage but a high voltage, a developing 400V oscillation that creates 22000 or more volts in the secondary of the spark coil.
Connecting a diode across the ignition coil instantly absorbs the energy stored in the spark coil inductance, kills the spark energy but will protect your points. The side-affect is no spark to the plugs.
A good dwell/tach circuit should just should sense voltage at the points-sparkcoil connection, not interfere with its operation, that's why I have suggested and offered circuits very early in this discussion to make an input buffer circuit.