Since I haven't been able to compile your game (missing wave.dcu) I cant pinpoint what exactly is the cause of slowdowns.
Also since it is some time since I used DelphiX I might be way off but I don't think calling
"Player.SpriteImage.LoadFromGraphic( Form1.PlayerGfx.Items.Items[Player.CurrentFrame].Picture.Graphic );"
is a good idea for changing player animation. Doesn't that reloads SpriteImage from memory to GraphicMemory?
The worst thing is that you are doing this constantly even if the Player frames wasn't changed.

BTW! Doesn't DelphiX offer a different way for sprite animations where you only change sprite animation position and don't need to reload it's graphic every time?