For "The Killer's," I think you could loosely interpret instances of Einstein's Relativity, but I think these interpretations are not that relevant and don't contribute to the meaning of the story or Relativity itself. The discrepancy about the clock's time probably has more to do with the restaurant owner pushing the time ahead to close earlier; or, the clock simply runs fast. This is probably the one element that lends itself to an analysis via Relativity. In other words, the malfunctioning clock does not really make a significant statement on special or general relativity (from the author's intent or a physics interpretation). We're talking near speed of light and quantum particles' position and speed being affected by light. However, I do think that the perceptual metaphors with respect to how people view the world do apply.
Broadly speaking, relativity and other related physics theories (like Heisenberg's Principle of Uncertainty) state that the universe is not static, mass curves space, time is measured differently for those moving relative to one another, mass amount changes relative to (high) speed, and the perceiver (this is the 'big general idea') perceives a reality relative to all these shifting interactions of time and space. That being said, the general conclusion is that each perceiver might see the same event differently - if he's moving at a different speed, the object he's viewing is moving at high speed, or if his perception is actually manipulating what he's looking at (Heisenberg). Again, these manipulations occur at speeds to high to be observed by people.
With respect to "The Killers" I think the question of relativity has much less to do with physics and more to do with the general implication of relativismthat each subjective individual can perceive a reality differently. For the narrator, Nick, his different perception is a question of 'moral relativity.' He finds himself in a situation where George and Sam are used to a world where hit men carry out their business with the casualness of selling oranges. Nick, the somewhat naive hero, is introduced to a new reality, filled with gangsters, killers, and regular people who are desensitized to this kind of violence (George and Sam).
Nick is generally bewildered by this. The confusion with the clocks and names (Henry, Mrs. Hirsh and Mrs. Bell) is not attributed to general or special relativity's warping of individual perception. It is more about finding yourself in a new situation or a new culture. Since it is new or unfamiliar, the new situation, culture, etc. will be different: relative to what you're used to.
I would only add this: Nick is a moral man, one who thinks the morals he believes in apply to everyone. This is the classical view of physics (Newtonian) that the laws of nature are immutable and everyone perceives them the same way. But Nick learns that he lives in a world of moral relativity: where, morality depends upon the individual or the society. Therefore, morality (and other ethical concepts) is not some immutable law that applies everywhere. This is where it is more like Einstein's relativity than Newton's idea of unchanging laws.
Try this one: