The way I see it, it's a made up rule by the fans.
Aside from Bayonetta, who got in because ballot, every single third-party in Smash is an iconic gaming character.
Sonic is well-known because of SEGA's rivalry with Nintendo during the 90s and is still going strong as one of the most well-known franchises
Snake is the mascot of both slealth video games and cinematic games (MGS games have so many cutscenes that they may as well be movies
)
Mega Man... well, he's kind of a has-been, admitedly, but he was still a huge deal in the 80s to the point of still being remembered today.
Pac-Man is one of the games that dominated the arcades in the 80s. Heck, if you have an arcade in your town, chances are there's a Pac-Man game in it today.
Ryu is the mascot of fighting games
Cloud is one of the most recognizable JRPG characters and a mascot of the genre