I don't know about that definition of rivalry. In the 10 times the Celtics won the Finals from 1959-1969, they Faced the Lakers 7, once before they moved to LA and 3 time back to back, one of those was a 3peat. Only once were they swept, when they were in Minneapolis, only once after that did it go less than 6 games and 3 times the full 7.
That may not seem like a rivalry to the Celtics who won every series, but I was old enough to remember at least the last 2 or 3. and although at that age I was a far bigger baseball fan than NBA fan, you can't tell me at least the Lakers considered it a rivalry, 7 trips to the Finals to be beaten by the same team every time is rivalry of epic proprtions to the losing side.
Boston versus Philly was no way a rivalry, based on the criteria mentioned earlier. Russell and Chamberlain may have been rivals but again, based on the criteria mentioned earlier, Boston had no rivals in the 60's, it didn't matter that Boston met the Sixers something like 4 or 5 staight times and lost to them only once, so if that is a rivalry, the Lakers/Celtics of the '60 is ABSOLUTELY a rivalry.
I would even say the Kings/Laker were a rivalry, albeit a shortlived one that only led to JoMal's drinking problem, but there was definately something there, maybe more fan based than team based but still...