Suponho que este seja algum tipo de problema de dependência, então aqui está minha árvore:

[INFO] Sikor:BrowserGame:war:1.0-SNAPSHOT
[INFO] +- junit:junit:jar:3.8.1:test
[INFO] +- org.springframework:spring-context:jar:4.1.1.RELEASE:compile
[INFO] |  +- org.springframework:spring-aop:jar:4.1.1.RELEASE:compile
[INFO] |  +- org.springframework:spring-beans:jar:4.1.1.RELEASE:compile
[INFO] |  +- org.springframework:spring-core:jar:4.1.1.RELEASE:compile
[INFO] |  |  \- commons-logging:commons-logging:jar:1.1.3:compile
[INFO] |  \- org.springframework:spring-expression:jar:4.1.1.RELEASE:compile
[INFO] +- org.springframework:spring-webmvc:jar:4.1.1.RELEASE:compile
[INFO] |  \- org.springframework:spring-web:jar:4.1.1.RELEASE:compile
[INFO] +- org.springframework:spring-context-support:jar:4.1.1.RELEASE:compile
[INFO] +- org.springframework.security:spring-security-web:jar:3.2.5.RELEASE:compile
[INFO] |  +- aopalliance:aopalliance:jar:1.0:compile
[INFO] |  \- org.springframework.security:spring-security-core:jar:3.2.5.RELEASE:compile
[INFO] +- org.springframework.security:spring-security-config:jar:3.2.5.RELEASE:compile
[INFO] +- org.springframework.security:spring-security-taglibs:jar:3.2.5.RELEASE:compile
[INFO] |  \- org.springframework.security:spring-security-acl:jar:3.2.5.RELEASE:compile
[INFO] +- org.thymeleaf:thymeleaf-spring4:jar:2.1.3.RELEASE:compile
[INFO] |  \- org.thymeleaf:thymeleaf:jar:2.1.3.RELEASE:compile
[INFO] |     +- ognl:ognl:jar:3.0.6:compile
[INFO] |     \- org.unbescape:unbescape:jar:1.0:compile
[INFO] +- org.thymeleaf.extras:thymeleaf-extras-springsecurity3:jar:2.1.1.RELEASE:compile
[INFO] +- nz.net.ultraq.thymeleaf:thymeleaf-layout-dialect:jar:1.2.7:compile
[INFO] +- org.hibernate:hibernate-entitymanager:jar:4.3.5.FINAL:compile
[INFO] |  +- org.jboss.logging:jboss-logging:jar:3.1.3.GA:compile
[INFO] |  +- org.jboss.logging:jboss-logging-annotations:jar:1.2.0.Beta1:compile
[INFO] |  +- org.hibernate:hibernate-core:jar:4.3.5.Final:compile
[INFO] |  |  +- antlr:antlr:jar:2.7.7:compile
[INFO] |  |  \- org.jboss:jandex:jar:1.1.0.Final:compile
[INFO] |  +- dom4j:dom4j:jar:1.6.1:compile
[INFO] |  |  \- xml-apis:xml-apis:jar:1.0.b2:compile
[INFO] |  +- org.hibernate.common:hibernate-commons-annotations:jar:4.0.4.Final:compile
[INFO] |  +- org.hibernate.javax.persistence:hibernate-jpa-2.1-api:jar:1.0.0.Final:compile
[INFO] |  +- org.jboss.spec.javax.transaction:jboss-transaction-api_1.2_spec:jar:1.0.0.Final:compile
[INFO] |  \- org.javassist:javassist:jar:3.18.1-GA:compile
[INFO] +- org.hibernate:hibernate-validator:jar:4.3.2.Final:compile
[INFO] |  \- javax.validation:validation-api:jar:1.0.0.GA:compile
[INFO] +- mysql:mysql-connector-java:jar:5.1.32:compile
[INFO] +- org.springframework:spring-orm:jar:4.1.1.RELEASE:compile
[INFO] |  +- org.springframework:spring-jdbc:jar:4.1.1.RELEASE:compile
[INFO] |  \- org.springframework:spring-tx:jar:4.1.1.RELEASE:compile
[INFO] +- org.springframework.data:spring-data-jpa:jar:1.6.4.RELEASE:compile
[INFO] |  +- org.springframework.data:spring-data-commons:jar:1.8.4.RELEASE:compile
[INFO] |  +- org.aspectj:aspectjrt:jar:1.8.1:compile
[INFO] |  \- org.slf4j:jcl-over-slf4j:jar:1.7.7:runtime
[INFO] +- javax.servlet:javax.servlet-api:jar:3.1.0:provided
[INFO] +- org.slf4j:slf4j-api:jar:1.7.5:compile
[INFO] +- org.slf4j:slf4j-log4j12:jar:1.6.1:compile
[INFO] |  \- log4j:log4j:jar:1.2.16:compile
[INFO] \- javax.mail:mail:jar:1.4:compile
[INFO]    \- javax.activation:activation:jar:1.1:compile

Pelo que descobri, o Spring 4.1.1 deve funcionar com o javax.servlet 3.1.0, mas estou recebendojava.lang.NoSuchMethodError: javax.servlet.http.HttpServletResponse.getStatus () I ao chamar response.getStatus () dentro do meu interceptador.
Ficaria feliz se alguém pudesse ajudar. Desde já, obrigado.

EDITAR: Web.xml adicionado

<?xml version="1.0" encoding="UTF-8"?>
<web-app version="2.5" xmlns="http://java.sun.com/xml/ns/javaee"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd">

    <servlet>
        <servlet-name>mvc-dispatcher</servlet-name>
        <servlet-class>org.springframework.web.servlet.DispatcherServlet</servlet-class>
        <init-param>
            <param-name>contextConfigLocation</param-name>
            <param-value>/WEB-INF/config/mvc-dispatcher-servlet.xml</param-value>
        </init-param>
        <init-param>
            <param-name>throwExceptionIfNoHandlerFound</param-name>
            <param-value>true</param-value>
        </init-param>
        <load-on-startup>1</load-on-startup>
    </servlet>
    <servlet-mapping>
        <servlet-name>mvc-dispatcher</servlet-name>
        <url-pattern>/</url-pattern>
    </servlet-mapping>

    <filter>
        <filter-name>springSecurityFilterChain</filter-name>
        <filter-class>org.springframework.web.filter.DelegatingFilterProxy</filter-class>
    </filter>
    <filter-mapping>
        <filter-name>springSecurityFilterChain</filter-name>
        <url-pattern>/*</url-pattern>
    </filter-mapping>

    <listener>
        <listener-class>org.springframework.web.context.ContextLoaderListener</listener-class>
    </listener>

    <context-param>
        <param-name>contextConfigLocation</param-name>
        <param-value>
            /WEB-INF/config/root-context.xml
        </param-value>
    </context-param>

</web-app>

EDIT2: Alterou o seguinte:

<web-app version="2.5" xmlns="http://java.sun.com/xml/ns/javaee"
             xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
             xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd">

para:

<web-app xmlns="http://xmlns.jcp.org/xml/ns/javaee"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://xmlns.jcp.org/xml/ns/javaee http://xmlns.jcp.org/xml/ns/javaee/web-app_3_1.xsd"
         version="3.1">

mas ainda estou recebendo o erro ao chamar response.getStatus ();