Technically speaking, any game that you just don't like can make you say "this game should not exist." Ever play Sonic '06? I'd imagine there's a fair number of people who would believe that the game shouldn't exist because of how horrendously bad it is.
However that's not what we're talking about, I suppose. From an artistic standpoint - that being a standpoint which one can find a game actually offensive - I'm sure there's plenty of people out there who would see a game like Hatred, for example, and say "This game should not exist because x, y, and z." They have the right to that opinion if they choose to hold such an opinion, but the fact of the matter is that the game
does exist...as such having such an opinion matters very little, and essentially just equates to "I really don't like this game."
In short, if someone walks up and says "This game shouldn't exist because I find it offensive", just tell them "Well cry me a river then build yourself a bridge and get over it." If we're going to declare videogames to be art - a notion I fully support - then there can't be any taboos, just as there aren't any taboos in any other form of art.
For example, I personally think Hatred is an incredibly stupid idea for a game...the entire concept was built to create a controversy engine that ensured it would sell well on launch day and I find that kind of controversy-whoring to be nothing but some developers making a money grab. Still, to remain consistent, it
is technically someone's artistic vision. So while I think it's incredibly shallow of the developers to make such a game, I'm not going to say that such a game shouldn't exist. In fact, I'm actually kinda glad it exists, because the next time a developer tries to come up with a scheme like that hopefully we'll all see through it.