Step 6: Press Start

Picture of Press Start
Press start to begin the first of many long video game sessions.
I had no idea that NES game cartridges were 8-track-tape based!
Not sure what you're referring to there, but I (and many others, I'm sure) can verify that there is absolutely no magnetic tape in a NES cartridge.  The problem the author is solving is directly related to the the pins in the cartridge no longer making good contact with the interface inside the NES unit.  By wedging the folded card (or any other shim, for that matter) between the cartridge and the slot it is forcing the cart into making contact with the internal pins.  The fix the author presents is a good temporary work-around but the only way to permanently fix the issue is to open the NES up and bend the pins in the cartridge slot back into their normal operating position.
It was a joke.  I'm rather old and when I wqas young there were 8-track tape players in cars.  Do you know how an 8-track was set up?  It was basically a magnetic tape around 4 times as wide as a cassette.  As the tape played, the head read two of the tracks, forming stereophonic sound.   Once it reached the end of the tape, the head moved to the next set of tracks.  Each tape had 4 channels consisting of two tracks each.  If you picture eight horizontal parallel lines one on top of each other, channel 1 consisted of the head reading lines 1 and 5, channel 2 read lines 2 and 6, etc.  The tape itself was a huge loop and when the tape came to the splice, that signaled it to change channels.  As the player or tape got old, we had to stick paper matchbooks between the tape cartridge and the player slot to act as a shim and get the tracks to properly align with the head.  Usually what would happen was the left speaker was playing songs from one channel and the right would be playing songs from another channel.  And the best song on an album (another long story: albums) would be split between two channels.
I get you there. While I wasn't around in their heyday, I remember 8-tracks - a friend of my parents had quite the collection. I never saw anyone jam a matchbook in between the cart and the slot to get it to play properly, which is why the joke just went *WHOOSH* over the top of my head.  Either way, it sounds like both methods are a temporary fix. :)