I think that the most obvious element about the short story being seen as a thriller is that it contradicts the reader's expectations.  Both inside and outside of the courthouse, I think that the "thriller" label would be assigned because it challenges the reader's understanding of what is to happen.  The trial is anything but ordinary, as Mrs. Salmon's testimony is revealed as lacking under cross and the rest of the witnesses recant their supposedly certain testimony.  Outside of the courthouse, the bus hitting one of the twins is an element that can be seen as a "thrilling" element simply because one is not ready for it.  I am not entirely certain, though, that this would constitute the story as one that resides in the "thriller" genre.  The ending of the story is impactful and does challenge the expected understanding of how the narrative will end.  Yet, I don't particularly see it as one that is more like a drama or a serial.  Rather, I think that Greene is simply seeking to make a statement that there is not much in human made construction that is absolute and beyond doubt.  The legal system is reflective of such an element, something seen as absolute and then winding up to be anything but.  The supposed exoneration of Mr. Adams is much the same way, something that is certain for all of five minutes until the anguish or death through the bus "hits" him.  It is in this thematic development that I am not entirely sold on the "thriller" aspect of the story.  Rather, I see it as more of a statement of the lack of totality that confronts human beings in this state of consciousness.  I sense that Greene is trying to make a thematic statement of being, one that overrides "thriller" genre considerations.