The general rule of thumb is that if the game gives a proper ending, it doesn't have to be the best ending. So in the case of the Sonic games, not getting the Chaos Emeralds would still count, as you still beat the game. There's exceptions - using the NES as an example, Double Dragon II would require the highest difficulty to be beaten because there isn't a proper ending unless you beat the game on hard. However, it would not be required to beat Bubble Bobble with two players because the "bad" ending for beating the end boss solo still constitutes an ending. I would say the best result is to go on a case-by-case basis, as it's impossible to forsee everything at this point.