A more relevant interpretation relates to Law 2 (the ball) and reads:
If an extra ball enters the field of play during the match, the referee must stop the match only if it interferes with play. Play must be restarted by a dropped ball in the position where the match ball was at the time when the match was stopped, unless play was stopped inside the goal area, in which case the referee drops the ball on the goal area line parallel to the goal line at the point nearest to where the ball was located when play was stopped.
In short, a drop ball should have been given on the edge of the 18 yard box because an extra ball (beach type in this case) interfered with play inside the penalty area.
The referee probably didn't remember this because unless you are doing a match on Mannington Rec or some other "parks" level, the chances of having 2 balls on the pitch at the same time are pretty slim. Not that that is an excuse for him - he messed up big time!
That's the first time I've heard anyone using that rule to explain why it should have been disallowed. I don't see how this rule can apply though as it is blatantly talking about another football rather than a beach ball so it would be a stretch to apply it in this case.
Also, are you sure it would be a drop ball on the edge of the penalty area? I thought a restart is only moved if the offence happens within the goal area (6 yard box), in which case play restarts on the edge of the goal area (not the penalty area). Not sure the chances of two balls on the pitch are that slim, I'd say its pretty common due to the widespread use of multiple balls in games nowadays.
I thought the consensus was it should have been disallowed under rule 5 - the power and duties of the ref, which says "the referee....stops, suspends or abandons the match because of outside interference of any kind". I'm not convinced by this rule applying either though. Its not a rule as such, more of a guidance stating the power of the referee and was it an outside influence - Reina had control of the beach ball and put it in the back of his goal, so is it any different to a keepers bag making it on to the pitch?
I reckon FIFA could do with adding a guidance note to the rules to cover this situation in the future.
