A fellow called James Elkins has written a book on the subject of being moved to tears by art. Or rather, not being moved to tears.

In the rest of the book, Elkins wonders aloud about his inability to cry in front of pictures - perhaps it's a deformation professionelle - and weaves a series of, by turns, touching and revealing narratives around the topic of tears and painting. Throughout, he remains quietly sceptical of his own project, announcing at one point that "I had nearly given up after receiving a letter from E.H. Gombrich". This letter, in slightly abridged form, comprises the ninth segment of correspondence reproduced in the appendix.
Gombrich, it appears, never wept in front of a painting and "hardly ever laughed", in spite of the fact that, as he points out to Elkins, he spent some considerable part of his career on the history of caricature. But what caused Elkins to become even more despondent was Gombrich's citation of a passage from Leonardo da Vinci to the effect that it is impossible to make people weep over paintings. As Elkins remarks: "What more is there to say after that? How could anyone cry unless they're a bit off in the head?" Well, he persevered, and in a curious way the persistence pays off since it illustrates, far more effectively and in much more down-to-earth ways, the difference between an emotive response to a work of art and an affective one.

This is the centre triptych of the Rothko Chapel which Elkins pays a visit to:

Elkins decided to visit the Rothko Chapel in Houston, since, although "there is no survey to prove it ... it is likely that the majority of people who have wept over 20th-century paintings have done so in front of Rothko's". He booked a flight and went to see the octagonal room, which is dedicated as an interfaith church in a quiet neighbourhood of the city. The "paintings looked worn and flat and dull - like pots scrubbed too hard with steel wool. They were weak and frail, like that dusty black fabric that is stretched over old audio speakers." Boredom was one of his initial responses and after some time inspecting the large canvases he felt great fatigue. [...]
Elkins points out that Rothko's paintings are almost unique in 20th-century art in attempting to convey, or indeed construct, private religious experience. Rothko commented in 1957: "The people who weep before my pictures are having the same religious experience I had when I painted them." And, according to Elkins, people have been weeping in galleries and museums ever since, when confronted by these darkly moving paintings. But weeping eluded Elkins - the closest he got to an excessive or out-of-control moment was when, having been inspecting one of the canvases at very close range, he "began to get a little dizzy".

I don't know, maybe you have to actually be there in the place itself, but if the photo is any indication there doesn't seem to be a lot worth shedding tears over. There's not even much worth reacting to, as far as I can see.