The comparison needs to be evaluated fully inside EL ${ ... }, not outside.
<c:if test="${values.type eq 'object'}">
As to the docs, those ${} things are not JSTL, but EL (Expression Language) which is a whole subject at its own. JSTL (as every other JSP taglib) is just utilizing it. You can find some more EL examples here.
<c:if test="#{bean.booleanValue}" />
<c:if test="#{bean.intValue gt 10}" />
<c:if test="#{bean.objectValue eq null}" />
<c:if test="#{bean.stringValue ne 'someValue'}" />
<c:if test="#{not empty bean.collectionValue}" />
<c:if test="#{not bean.booleanValue and bean.intValue ne 0}" />
<c:if test="#{bean.enumValue eq 'ONE' or bean.enumValue eq 'TWO'}" />
By the way, unrelated to the concrete problem, if I guess your intent right, you could also just call Object#getClass() and then Class#getSimpleName() instead of adding a custom getter.
<c:forEach items="${list}" var="value">
<c:if test="${value['class'].simpleName eq 'Object'}">
<!-- code here -->
</c:if>
</c:forEeach>