Reading the website, I absolutely would have interpreted the breakdown to mean that the winner gets $1,800. That obviously is what they meant because they sent you a check for the full amount. If it was just that you were confused about the prize money because it wasn't clearly worded on the website, your confusion wouldn't cause them to produce a check in the wrong amount.
This is all a mistake on the RD's part. No big deal, everyone makes mistakes. But own it and fix the problem. If I was the RD, I'd say "I screwed up," and I'd cut a check to cover the difference between the intended prize money and the prize money that was actually awarded.