Ok. So, when you launch the game, it just extracts the files from the .rar and then closes. To actually play it (after you click "launch" to extract the files) you have to go to your appdata roaming folder (search for %appdata% on your computer), go into the "itch" folder, then the "apps" folder, then the "archipelago" folder, but the application there isn't the game itself. Open the folder also named "archipelago" inside that folder and that's where the game is.
This happens with any .rar file you download from the web, if you don't save the .rar file to a location of your choosing but instead choose to just open the .rar file when it has finished downloading. Then the default destination path for extraction is C:\Users\YourUsername\AppData\Local\Temp\Archipelago.
But if you choose to save the file instead of opening it, then it goes to your downloads folder (default is C:\Users\YourUsername\Downloads) and when you then extract the files, the default path is C:\Users\user\Downloads\Archipelago.
From there on you still need to extract the actual game from the Archipelago.exe file with blue icon. This is an unnecessary step which I could've avoided, but I pretty much just copied the process from an igmc 2017 entry which had success in the competition.
Hopefully this clears things up a bit :) But if someone has problems just hit me up and I'll be more than happy to help out!