"The loss of one stock from one or both players" means that if, in one simultaneous or approximately simultaneous event, both players lose a stock, or if the players fight until one loses a stock and the other stands victorious (for that game, at least), the game ends. The set resumes when the player who lost the stock descends from heaven on a cloud, offering the opponent who just scored a kill a brief respite before the next game begins.
You can start a game at a disadvantage, namely being at a high % (or asleep lolz), much like in tennis (though I am not even trying to compare smash to tennis otherwise) where one competitor gets to serve, which has decided advantages.
Also, fun fact: In SSB64 and the Japanese version of melee the announcer says "game set," implying that the victor won the final game to take the set. He is not saying "the outcome of this game is set!"