The Open Mind Prize, and presumably many other prizes in mathematics and different fields, makes the list of a few (in this case: three) nominees public before the prize is awarded. Suppose that a person was among the shortlist of nominees but was not awarded the prize. Is it reasonable to mention this on their CV? On one hand, being on the shortlist is presumably a form of recognition. On the other hand, being nominated but not winning may be seen as negative.
It is fine to list your presence on the shortlist, since that list was published by the awarding group. I would say otherwise if there was no clearly public record and the finalists were merely privately notified.
But the group itself has seen to honor a few candidates separately from all nominees and you can make a note of that.
Not essential, but reinforcing, is the fact that the three "finalists" are asked to present a special lecture at the conference. Congratulations.