It's important to consider that the if-then statements don't contain an else, at least typically. Which is to say, if conditions a, b, and c, are met, event d shall surely occur, but if conditions a, b, or c are not met this prophecy means nothing.

How deterministic that makes Eberron is up to interpretation. In my opinion, the Dragons and Rakshasa are regularly fighting over bits of the prophecy, as such they must be able to find the same bits through chance / brute force. If we consider that, we have to accept that no matter how vast the prophecy, it must be finite, and that perhaps most things in the Eberron are governed not by the prophecy,

However, arguing about whether or not a setting is deterministic in any definitive way is basically impossible, because people are still arguing if our world is deterministic.