So, GanttProject runs with Java 8 from any vendor. However, our dear vendors at the moment can’t agree on standard registry keys where Java launchers (native Windows executables which essentially search for required Java runtime and launch Java machine) can find them. If launcher can’t find any good Java runtime, it shows you the message.
GanttProject 3.0 will come with bundled Java runtime which will make this process more smooth. Meanwhile, you can try running ganttproject.bat which works with any vendor, provided that java executable is reachable from the user PATH variable (a set of folders where windows searches for executable files). I hope that most vendors put their java.exe into a folder which is registered in PATH.
See instructions on installing from ZIP for more details