In local leagues you may be able to continue with less than 7 but for a FIFA sanctioned event like the World Cup it is definitely 7. Here is an bit from FIFA's Laws of the Game:
Although a match may not START if either team consists of fewer than seven
players, the minimum number of players in a team required for a match to
CONTINUE is left to the discretion of member associations. However, it is the
opinion of the International F.A. Board that a match should not continue if
there are fewer than seven players in either team.
This is where the context is just odd. It is clearly stated by IFAB that it is an opinion, and not a rule, per se. The fact is it was a ridiculous call that was brought about by the idiocy of the ref. Although I understand where you are coming from with having a game stop with less than 7 players, a move where players committed so much dissent toward the ref to force a decision on a game would make it so that FIFA would have to take a hard look at this issue.
How weird would it be to have a game called with a one goal deficit b/c the players are standing up to a horrible call, with absolute justification for doing so? How much crap would FIFA have to go through to explain why a game was stopped? I would almost guarantee that an unprecedented move like that would have to call into question the integrity of the laws of the game, and maybe create some future change in the process. The team that the phantom call occurs against is the one who gets punished the most. The ref may get punished from the standpoint of not working a game in the next round. The player who dove gets no punishment. None of that makes sense to me, unless the ref was gaining some level of favor in doing so, which would also bring some level of speculation on FIFA's management.
Great World Cup so far, minus the awful officiating in the first two games (Brazil-Croatia and Mexico-Cameroon). Everything else for the refs appears to have settled down, and the play has really been awesome. Lots of excellent goals. Maybe CONCACAF has shown it is gaining strength with the Costa Rica win over Uruguay.