Yes, quite right.
Looks like some one has done an engine swap at some point in time and the new engine had a different plug to the old so they cut it off & joined the wired.
Best guess is the 4 wire plug wasoff a mower that h=used AC headlights.
Next, the magneto is self powering and has nothing to do with the wiring apart from turning it on or off by grounding the kill wire.
A poor spark will be caused by either a bad ground contact between the coil & the mower, a weak magnet in the flywheel, coil fitted upside down ( might even not work ) , too large a gap or wrong coil.
Also the spark is speed dependent, the faster the flywheel spins the bigger & fatter the spark.
Easiest way for you to verify if the spark is OK is to get a 3 contact spark tester, fit it to the plug and crank engine in a dark place.
If the spark can not jump the widest contact you have problems.
If it does jump the the problem is with you not the mower.