If wine is not displayed as an option even when you click "all applications", download the mac download files instead simply for the wine gecko and mono packages. Then delete the folder and try opening the .exe with wine again.
Don't double post, ahh
Edit: Pandorox contacted me and we are trying to solve the problem together. All of you Mac users, if you know any solutions or anything else - please, post here or contact me via PM. If we ever find a solution, it will be posted right here.
