Disclaimer: I know nothing about either iTunes or poker sites; so, I can't really say if wine is the best approach or not.
For wine, though, in general, when you double-click on an exe file, wine automatically opens and launches it. If there is a program that you have installed -- IE, you clicked on an exe file, which installed a program, and now you're looking to find the program and launch it -- you can check the wine directory, which is usually: /home/<username>/.wine/drive_c/Program Files. Note: there's a dot (.) before the "wine", meaning this directory is hidden; so, choose view hidden files in your file manager to see this directory.