I have not studied this galaxy cluster specifically. However, I can speak about systems like galaxy clusters that have a large number of bodies that are in close enough proximity to have a non-negligible gravitational effect on each other. For any such n-body system, where n is large (a solar system, a galaxy, a galaxy cluster,...), it can be assumed that, 1. there is a net angular momentum of the system, and 2. it is reasonable to assume that this angular momentum is non-negligible. I state 1 and 2 based on the following (very general model of solar system and galaxy cluster formation).
Such n-body systems form by the collapse of a very large amount of gas, dust, and other minerals. When fully extended, these clouds are cold, the the velocities of any given molecule or atom in them is comparatively slow. However, it is very improbable that the total angular momentum of the cloud of gas is zero, and more importantly, that it is close to zero. From this point, it is easy to reason that, so long as no angular impulse is applied to the system and no mass is added or removed from the system, the gas cloud can collapse or disperse in whatever way is consistent with the conservation of angular momentum, and the angular momentum of the system will not change. Thus, a galaxy cluster like Abel 1689 should have a non-negligible angular momentum.
But I have skipped over the most important logical step in the above argument. I simply assumed again that the angular momentum of the gas cloud would not be even close to zero, effectively shifting the level of the explanation up one level. Unfortunately, the best answer to "why do the gas clouds have non-negligible angular momentum?" requires explaining where the gas clouds came from. The extent of my understanding here is that the gas clouds that formed galaxy clusters only existed during the very early universe. Once they collapsed into galaxies, there is no process that could have caused a galaxy cluster (or even a galaxy) to disperse so completely that it forms a new very low density gas cloud that can re-collapse. Thus, the gas that made the galaxy cluster must have had an angular momentum if the galaxy cluster system is to have angular momentum.
I do not know if the sum total of the angular momentum in the universe is said to be zero or some finite value. However, I do know that even if it is zero, localized regions of matter in a system that has zero angular momentum do not also need to have zero angular momentum. Thus, the Abell 1689 system could be one such local region with non-zero angular momentum.
Continuation: According to The Cosmic Perspective: Seventh Edition, when considering galaxies that have not yet collided with another galaxy, the initial angular momentum of the protogalactic cloud is a large contributor in determining if a galaxy will be spiral or elliptical galaxies.
Regarding elliptical galaxy clusters, TCP has this to say: "Observations of galaxies in clusters support the idea that at least some elliptical galaxies result from collisions and subsequent mergers. Elliptical galaxies dominate the galaxy populations at the cores of dense clusters of galaxies, where collisions should be most frequent. This fact may mean that any spirals once present became ellipticals through collisions."
Thus, TCP suggests in this paragraph that at least certain clusters contain dense cores of elliptical galaxies that resulted from collisions and mergers of galaxies that had markedly different angular momenta, resulting in a new galaxy that has much less angular momentum.
But this doesn't really answer your question either. I have looked also for scholarly articles to find some consensus on what the typical angular momentum characteristics are, and found very little. Most discussions of galaxy cluster formation discuss filament formation and collapse. The one article of note I found was from Tom Crawford at the University Of Chicago:
"The most obvious and uncontroversial class of structures beyond the galaxy is the galaxy group or cluster. These structures consist of tens to thousands of individual galaxies that are bound by gravity to one other and orbit a common center. That center is not defined by some huge central object, as the Sun defines the center of our solar system, but instead by the center of all the mass in the cluster, including dark matter. In fact, the dark matter dominates the mass budget of galaxy clusters, outweighing the normal matter by about a five-to-one ratio."
This description suggests more than just "random" motions of gravitationally bounded objects (galaxies), but does not definitively say anything about the net angular momenta of these systems.