I have created a new easy way to download. It should be up now on my project page (https://arenjames.itch.io/perfect-pitch-training)
Just download and unzip all files in the same folder.
The *.jar file is an executable file of Java. So if you have Java installed it should go.
If the unzip program you're using recognizes this as a compressed package then you can open it with a Right click -> "Open with" and select the Java one.
If it cannot be executed or you cannot find the entry in the "Open with" Menu, although you have installed Java, you may try to run "java -jar ItchIOMusicJam.jar" from the command prompt at the folder with the jar file in it. Or you may create a batch file in the same Folder as the files with the content "java -jar ItchIOMusicJam.jar" and then double click that batch file.
For me the first easiest part works fine, I don't know why you can't start yours, but I would appreciate it if you give it one more try :)
LG arenjames