Dúvida no Ex. 1 da Aula 4 - Filtrando requisições - ServletRequest cannot be cast to javax.servlet.Servlet

Bom, praticamente copiei o codigo criado na explicação e coloquei para rodar depois de ter seguido o video mas o problema de cast continua a ocorrer.

import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
import javax.servlet.annotation.WebServlet;
import javax.servlet.http.HttpServletRequest;

@WebServlet (urlPatterns="/*")
public class FiltroDeAuditoria implements Filter{

    @Override
    public void destroy() {
    }

    @Override
    public void init(FilterConfig config) throws ServletException {
    }

    @Override
    public void doFilter(ServletRequest request, ServletResponse response,
            FilterChain chain) throws IOException, ServletException {
        HttpServletRequest req = (HttpServletRequest) request;
        System.out.println(req.getRequestURI());
        chain.doFilter(request, response);
    }

}

Inclusive estou importando o javax.servlet.filter que é o utilizado, mas ele da crash quando qualquer coisa é acessado e mostra o seguinte stack:

java.lang.ClassCastException: br.com.alura.gerenciador.web.FiltroDeAuditoria cannot be cast to javax.servlet.Servlet
    at org.apache.catalina.core.StandardWrapper.loadServlet(StandardWrapper.java:1095)
    at org.apache.catalina.core.StandardWrapper.allocate(StandardWrapper.java:817)
    at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:135)
    at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:106)
    at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:502)
    at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:142)
    at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:79)
    at org.apache.catalina.valves.AbstractAccessLogValve.invoke(AbstractAccessLogValve.java:616)
    at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:88)
    at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:518)
    at org.apache.coyote.http11.AbstractHttp11Processor.process(AbstractHttp11Processor.java:1091)
    at org.apache.coyote.AbstractProtocol$AbstractConnectionHandler.process(AbstractProtocol.java:673)
    at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.doRun(NioEndpoint.java:1500)
    at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.run(NioEndpoint.java:1456)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
    at java.lang.Thread.run(Unknown Source)

o que fazer?