According to your Servlet, you should probably call http://localhost:8080/gameResult/logout
instead.
<a href="logout">Logout</a>
You could add automatically context to elimitate further problems if you use this code in another path, this way you won't have to bother about relative path.
<a href="${pageContext.request.contextPath}/logout">Logout</a>
Also, you should remove this stuff from web.xml
:
<servlet>
<servlet-name>LogoutServlet</servlet-name>
<servlet-class>org.sample.servlets.LogoutServlet</servlet-class>
</servlet>
<servlet-mapping>
<servlet-name>LogoutServlet</servlet-name>
<url-pattern>/logout/*</url-pattern>
</servlet-mapping>
Because you are using WebServlet
annotation.