The desktop route is (almost) impossible, because it's different for every linux distribution. It typically works the other way round: Linux distro maintainers will pull open source software from the developer's repositories and integrate them into their mechanism. Your way, distributing commercial software in binary form, is a fringe case. It's not typical.
There are no commercial programs that work on every distro's desktop, they typically concentrate on one or two and let the users themselves deal with the rest. That's one of the reasons why linux is so small outside the server world.
I would just let the customer start via terminal and be done with it.
Thanks for all the explanations. I really know nothing about the Linux.
As to your second question: I have no idea about the links.
In the application that you open through the terminal you will find several buttons among them: image1/image2/Sound. When I try to open these assets through the application, nothing happens, but I can do it normally in the windows versions. Do you know why I cannot do the same in the Linux version?
Taking advantage of your patience, I wonder if you think that is better if I will create a browser version to the Linux users. The problem is that application needs to work in offline mode. In this case, the user will need to access the app online in the first time and use the offline cache in the next times, right?