Highly unlikely in the OP's case because most likely they are talking about one of the much more common vision statin lawn mowers of the past 25 or so years which don't have that feature anyways..
The engine you pictured is of the mid 80s probably at newest with quite a few different designs in it. Lol
The thing about basically all the safety switches on mowers, and even vacuums and blowers and things that have extra safeties for shoots, discharges etc is once you take the shroud off and get to the actual coil, all you have to do is remove the small kill switch wire on the coil and then none of the other safeties matter at all because it disables everything and the the vast majority of all small outdoor power engines like this use whatever kill switches they may have to go right back to this wire to do the same end result.
So you pull one wire, you eliminate them all for test purposes.
It is common to have one of your other safeties causing a no start or even no crank condition on some of the smaller riders because they add extra ones like this.
I've had the leaf vac chippers come in multiple times with the rear discharge button not being pushed down because the plastic / metal tab that presses on it tweaks over the years and doesn't push down enough.
I'm also seen another style with one over on the side that was messed up and I've seen plenty of the rear engine riders mostly of the MTD manufacturer and the Craftsman r1000 which is also made by them where the discharge shoot or mulch cover isn't pressing on that plunger safety switch because it's bumped into something so the machine won't crank.
Then you have the low oil shutdowns on generators which can also create a problem.
But with all these situations if you're testing, when you get to the actual coil and remove the wire, it has no choice but to spark when you spit it if the ignition module is working because you have eliminated all forms of kill switch which would be grounding out the coil which is all it does anyways as far as spark goes. On the rear engine riders I mentioned it's actually part of the electrical system and not the kill switch system because it prevents it from cranking just like parking brake switch and the blade engagement switch would do so it really has nothing to do with spark and on most all of these, if you could mainly crank the engine in this fault condition it would still start and run but since it's electric start only there's no way to crank it as it disables the starting switch solenoid circuit.