This coil is used in an engine without a spark plug. It will have an ignitor which is essentially a set of points inside the combustion chamber that produces a hot spark when the points open. Often the primary winding of a T coil is used to do the job of your coil.
The whole system usually consisted of the points, a coil & several dry cells. NO condenser. The points are tripped by the valve linkage.
Yes the Quadracycle has an internal spark. The two plugs will have electrodes forming a gap inside the cylinder like an oil burner or a 1 cylinder Cadillac. The spark is timed by the insuilated bar linked to the exhaust valve rocker arm.
There have been reproduction cars built using a regular spark plug.
The coil pictured in this thread would not work on this system.