This logo rules;
Its a 4-way split to denote the 4 player battle royale gameplay
as well as being an "X-over-O," to denote the theme of Smash being the Ultimate cross(X)-over(O).
It works even better now than it did in 1999, honestly.
Were either of these actually designer's intent? They both sound like a stretch to me.
Even if they're both legit, the logo itself communicates absolutely nothing to a viewer who isn't familiar with the game. Hell, as people in this thread have shown, it's inscrutable even to people who are familiar with the game. It could be the logo for just about anything; a laundry detergent, a government department, a car brand, an employment agency. It's an absolute nothing of a logo; a void of personality.