I have an app engine project in Eclipse. I have kept a JSP file in WAR folder. I have given the path in the installed jre as JDK1.8
As per the documentation available, "App Engine runs your Java web application using a Java 7 JVM in a safe "sandboxed" environment.". So that is as far as the runtime is concerned. It does have a backward compatibility for Java 6 applications for now.
However, keep in mind that the App Engine SDK now supports only Java 7. And ideally I would not go with JDK 8, where things are still in the works.
Behind the scenes, when you upload your application to App Engine, they know which Java runtime to use based on the SDK JAR that you have linked. So ideally, that is taken care of for you.
So, I still believe that though you have provided JDK 1.8 locally, the App Engine version JAR will be enough for Google to deploy your application in an appropriate Java 7 JVM and things should have worked if it is just a simple JSP that you are trying to link up.
Since you have not given details on what the JSP does, it would be good to know that since that could give some pointers. Additionally, I suggest that you allow for DEBUG logs and visit the Admin Console logs to understand what is going wrong. That will give you more details.
I had exactly this problem; including even one JSP file, even with no Java code or any content at all, would prevent my appengine instance from starting.
The solution was to make sure you start Eclipse using the 1.7 VM, even if you're developing against the 1.8 JDK. Because my Eclipse instance was running in the 1.8 VM, the generated JSP files were incompatible with AppEngine.
You change the host VM in the eclipse.ini as shown here: Google App Engine JSP can't deploy: java.lang.RuntimeException: Cannot get the System Java Compiler. Please use a JDK, not a JRE