I think whether it's okay for a game to be fair or not is up to the person playing it. Overcoming insane odds when the game is trying to beat you to a pulp and maybe even breaking it's own rules to do so can be enjoyable to some, but absolute torture to others. I personally don't mind it all that much as long as the game itself gives you the idea that you have the odds stacked against you, and it's not going to be easy or even fair. Or if it's optional, like "Hell and Hell" difficulty from Devil May Cry 4. This is a difficulty setting where you die in a single hit from anything, you yourself do less damage, and the enemies and bosses have around 175% of their normal health. Does that sound fair? The answer would be no, but I found it insanely satisfying to beat the game on that setting.
As for the first Dark Souls mimic being unfair, I strongly disagree with that. The first mimic you encounter is in Sen's Fortress, a place that literally a few steps in has a trap in the middle of the floor. A bit further in and you're presented with a room filled with giant swinging blades and very narrow walkways. You get the impression that this place exists to kill you, and it's going to try it's hardest to do so. With that in mind, when you reach the room with the mimic you'll notice the chest is sitting in the middle of the room. The other chests in the game are placed pretty neatly, often against a wall. This one is sitting at an awkward angle in the middle of the room, and if you look at the chest for a few moments you'll notice a few differences. This chest has a different looking lock, the chain on the right side of it is straight compared to the half circle shape the chains on the other chests make, and you can also see that the chest is breathing. Also if I remember correctly the mimics were a slightly different color, although I'm not entirely sure of that. But even if you don't stop and notice that the chest itself looks different and is breathing, it's awkwardly placed in the middle of a room in a building filled with traps. Sen's Fortress tells you just from the first few rooms that it's filled with traps and is designed in a way that if you're not careful and watch your surroundings carefully, you're going to die again and again. The game gave you the warning signs in how the chest looked, how it was placed, and the environment that it was in.