This section is about the program as a whole and not the specific files you mentioned in the question.
You are using publicly available libraries rather than writing all of the solution yourself, this is very good.
You are using GitHub for source control and that is also very good. Since you are using GitHub for source control you should ...
Welcome to codereview.se and thanks for sharing your code.
Here is what I think about it. Please keep in mind, that this is my personal view on it.
Do not use the Java Singelton pattern.
The singelton pattern is just another name for a global variable, which we consider harmful and bad coding since the early days of programming.
Also the pattern is not that ...
It looks like pretty good procedural code overall.
int i, j; // CONTATORI
These indices can be local to functions. Globals are fine, but not in this case.
Also sposta is probably always local to movimenti() function.
void stampaBordi() // STAMPA LA CORNICE DEL CAMPO DI GIOCO
Always write source code and comments in English (I'm not a native English speaker either). You will sooner or later need to share code with other people around the world, like you just did here and now. Therefore it needs to be in English.
More importantly still, learning two technical programming terms for everything when you only need to learn one is ...
Some suggestions in no particular order:
Organize your header files.
I like to group related things together. In this case, "standard" versus "OS specific". I also default to sorting things alphabetically/asciibetically if there is no reason to do otherwise.
Group related things: functions with functions, variables with variables. Don't ...