The sentences can be explained with the help of the fuller context:
I speak to Lisa and Lisa speaks of parallel crying, the crying that comes alongside art but not precisely from it. Plot does not jerk the tears from you; some other force corresponds. This pleases me, as I have always preferred parallel lines to perpendicular ones. Perpendicular lines are Chekhovian; the introduced gun goes off. Parallel lines are Hitchcockian; the present bomb is enough.
As Ray Butterworth says in his answer, Chekhov's gun is the well-known principle of dramatic economy: a work of art should have no extraneous elements. Anton Chekhov often used the metaphor of a gun to express this idea. For example, in an 1889 letter to Aleksandr Semenovich Lazarev, he wrote:
One must not put a loaded rifle on the stage if no one is thinking of firing it.
Quoted and cited by Isiah Berlin, berlin.wolf.ox.ac.uk/lists/quotations/quotations_by_ib.html. Accessed 18 January 2021.
In contrast to Chekhov, Alfred Hitchcock often spoke of the effectiveness of a threat that doesn't materialize. In his series of interviews with François Truffaut, Hitchcock contrasts suspense and surprise:
There is a distinct difference between “suspense” and “surprise,” and yet many pictures continually confuse the two. I’ll explain what I mean.
We are now having a very innocent little chat. Let us suppose that there is a bomb underneath this table between us. Nothing happens, and then all of a sudden, “Boom!” There is an explosion. The public is surprised, but prior to this surprise, it has seen an absolutely ordinary scene, of no special consequence. Now, let us take a suspense situation. The bomb is underneath the table and the public knows it, probably because they have seen the anarchist place it there. The public is aware that the bomb is going to explode at one o’clock and there is a clock in the decor. The public can see that it is a quarter to one. In these conditions this same innocuous conversation becomes fascinating because the public is participating in the scene. The audience is longing to warn the characters on the screen: “You shouldn’t be talking about such trivial matters. There’s a bomb beneath you and it’s about to explode!”
In the first case we have given the public fifteen seconds of surprise at the moment of the explosion. In the second case we have provided them with fifteen minutes of suspense.
Truffaut, François. Hitchcock/Truffaut. With the Collaboration of Helen G. Scott. 1966. Revised Ed. New York: Simon and Schuster, 1984. pp. 181–182.
Later in the book, Hitchcock emphasizes that having the bomb actually go off is a mistake. Speaking of his movie Sabotage (1936), Hitchcock says:
I made a serious mistake in having the little boy carry the bomb. A character who unknowingly carries a bomb around as though it were an ordinary package is bound to work up great suspense in the audience. The boy was involved in a situation that got him too much sympathy from the audience, so that when the bomb exploded and he was killed, the public was resentful. (pp. 273–274)
Heather Christie says that in the Chekhovian case, the audience's emotions are engaged because of what actually happens: someone picks up the gun and shoots. The audience's reactions intersect those of the characters in the play: they are shocked and distressed at the shooting. The crying comes from the plot itself. In the Hitchcockian scenario, on the other hand, the action is almost irrelevant. The mere presence of the bomb, whether or not it goes off, is enough to engage one's emotions. The audience's emotions are on a parallel track to those of the characters, and the two sets of emotions do not intersect.
Christie is making a broader point about how art works generally. We assume that art elicits emotions; that what moves us is a quality of the artwork itself. Christie argues, however, that what "jerk[s] the tears" is not the artwork itself, but "some other force." That force is the emotions we invest in a work of art. Christie is contrasting tear-jerkers, which seek to manipulate the audience's emotions through melodramatic plot elements, with more authentic artworks that engage the spectator's or reader's emotions without manipulating them. Chekhov's gun is predictable, Hitchcock's bomb unpredictable. The latter's unpredictability opens up possibilities. A true work of art allows engagement without dictating the terms of that engagement "precisely."
While her broader point is well taken, I do not necessarily agree with Christie that in Chekhov's case, the crying comes from the art and in Hitchcock's, alongside it. After all, the presence of the gun is also suspenseful, and the unexploded bomb is also a plot element. Hitchcock's skillful deployment of suspense seems no less intended to elicit certain reactions from the audience than Chekhov's. Predictable art being perpendicular and the art of possibilities parallel is a good metaphor, but whether Chekhov and Hitchcock themselves fall squarely into those respective camps is debatable. Given Christie's highly compressed expression of a complex aesthetic argument, however, Chekhov's gun and Hitchcock's bomb work well enough as shorthand—with the caveat that the argument should not be taken as a summary judgment on Chekhov's art or Hitchcock's.