And yet, on that very same page: "This symbol is your assurance that the product has been evaluated and licensed by Nintendo." What part of this confuses you? Do you not understand the word "evaluated"? Yes, Nintendo has their own in-house quality assurance testers that will play through a game and send bug reports back to the developer/publisher. Sony and Microsoft do exactly the same thing. And they all rank the bugs they find according to how serious they are. Any "Must Fix" issue MUST be fixed before they will allow the game to come out on their system. They also have rules for just how many minor issues they will accept before the game will be allowed to release. And if they reject a game, the developers will have to fix the problems and submit it for evaluation again. This is in fact exactly why Day 1 Patches exist. The system owner rejected the game, but the company argues that they have contractual deadlines and they can't delay the release date, and they promise to have a patch out to fix these issues immediately upon release.
And the system of them looking over all games before release can indeed be subjective, and even overly harsh. Like famous stories of where Nintendo of America forced Power Blade on the NES to change their graphics from "anime" to "Schwarzenegger". Or how Sony of America used to hate all 2D games, and rejected tons of RPGs and fighting games. But regardless of subjectivity, having someone actually playtest every game helps immensely. Even bottom-shelf stuff like, say, Jekyll and Hyde, is still leagues above trash like Cheetahmen. In fact, could you imagine if every game from Action 52 came out individually on the NES, and flooded out all the good games? And then even more terrible crap came in because there was no barrier preventing it? Because that is exactly what killed the Atari, and almost killed all of gaming in the US, period.
And not only did their "Seal of Quality" system work to ensure that their games were decently fun, but every single other company did it afterwards. Sega had their own Seal of Quality icon for the Genesis, if you've never noticed. And, as I mentioned above, these quality checks from the system owners continue into the modern day, except usually not with an actual graphic icon anymore. Because today it's even more draconian than back then. Sure, some developers used to complain about Nintendo approval and try to release their own unlicensed games, but in this online age it's almost impossible to put anything on the PlayStation without Sony's approval. They can shut it down in minutes. There's no need for a seal icon to prove anything. The game HAD to be approved by them.
And if you still don't want to believe all these people who know better than you, then feel free to compare console games with mobile games. Mobile games are what you described, and has nobody running quality control at all except "Does it install?" and "Did it pass the virus check?" See the difference?