Yes, the leaderboard is only for the Windows version of Fish Tycoon - the other versions don't have that capability. The scores are automatically uploaded to the server when a player clicks on the refresh button of the statistics screen in the game.

To be blunt about it, many of those scores are not possible without cheating. There has been a lot of discussion about that, some of it heated. You could easily find it by searching the Fish Tycoon forum, if you're interested. Arthur does clean up the stats, but there is a flood of them coming in at any given time. He is considering various ways to improve the situation.