What I want to achieve is to install in a Linux (Ubuntu based) machine Microsoft Solitaire Collection. And as this application is a Window 10 Store App, my question is: is this really possible? If so, how?
Windows "Apps" are already executable by default but to answer your question, no you can't take a Windows program and install it in a Linux operating system.
The closest thing to doing something like this would be to install wine and have it work through wine, assuming the application is compatible which is most likely not the case for "Microsoft Solitaire Collection".
You can look at the following related question: http://askubuntu.com/questions/675260/is-there-an-ubuntu-solitaire-that-works-like-the-windows-7-game
You can also install games that resemble what you were looking and were created for your operating system or even get the "vanilla" version of Windows solitaire and run it through wine.