EDIT The problem is that you had two servlet mappings in your web.xml. I commented out one of them :
web.xml
<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/j2ee" xmlns:web="http://java.sun.com/xml/ns/javaee" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd" id="vaadinpokus" version="3.0">
<display-name>vaadintest</display-name>
<description>...</description>
<context-param>
<description>Vaadin production mode</description>
<param-name>productionMode</param-name>
<param-value>false</param-value>
</context-param>
<servlet>
<servlet-name>myservlet</servlet-name>
<servlet-class>com.vaadin.server.VaadinServlet</servlet-class>
<init-param>
<param-name>UI</param-name>
<param-value>com.example.MyVaadinUI</param-value>
</init-param>
<async-supported>true</async-supported>
</servlet>
<servlet-mapping>
<servlet-name>myservlet</servlet-name>
<url-pattern>/*</url-pattern>
</servlet-mapping>
<!--<servlet-mapping>
<servlet-name>myservlet</servlet-name>
<url-pattern>/VAADIN/*</url-pattern>
</servlet-mapping>-->
</web-app>
Now it should work. Thank you for sharing your code. It's easier this way to debug apps.