I started playing around with this. So far I'm planning to have a config option that lets the user switch between "Short name" and "Pronoun" as the source for the job type column.
This switch will only be available on Jenkins version 1.519 and higher.

Unfortunately I can't test the template plug-in. Is there any other way, apart from the pronoun, to find out if a job is a template (e.g. class/simple name)?

Template job instances internally are regular e.g. free-style jobs, but they have a JobProperty specifying the template and its parameters. Sample job (basically an empty freestyle project with equally empty template):

<?xml version='1.0' encoding='UTF-8'?>
<project>
  <actions/>
  <description></description>
  <keepDependencies>false</keepDependencies>
  <properties>
    <com.cloudbees.hudson.plugins.modeling.impl.jobTemplate.JobPropertyImpl plugin="cloudbees-template@3.17">
      <instance>
        <model>TestTempl</model>
        <values>
          <entry>
            <string>name</string>
            <string>jobname1234</string>
          </entry>
        </values>
        <item class="project" reference="../../../.."/>
      </instance>
    </com.cloudbees.hudson.plugins.modeling.impl.jobTemplate.JobPropertyImpl>
  </properties>
  <scm class="hudson.scm.NullSCM"/>
  <canRoam>true</canRoam>
  <disabled>false</disabled>
  <blockBuildWhenDownstreamBuilding>false</blockBuildWhenDownstreamBuilding>
  <blockBuildWhenUpstreamBuilding>false</blockBuildWhenUpstreamBuilding>
  <triggers/>
  <concurrentBuild>false</concurrentBuild>
  <builders/>
  <publishers/>
  <buildWrappers/>
</project>

But I doubt it's a good idea to rely on such internals!

—

I'd be willing to test snapshots of your plugin, and can also build them myself if you tell me the repo/branch.

Note that Cloudbees requires just an email address for a trial license allowing you to test your plugin with templates. And Templates 4.0-beta-x and Custom Update Center Plugins also introduce a whole bunch of new TopLevelItems that might be useful to support in this column.

Code changed in jenkins
User: Fred G
Path:
src/main/java/jenkins/plugins/extracolumns/JobTypeColumn.java
src/main/resources/jenkins/plugins/extracolumns/JobTypeColumn/config.jelly
src/main/resources/jenkins/plugins/extracolumns/JobTypeColumn/config_de.properties
src/main/resources/jenkins/plugins/extracolumns/Messages.properties
src/main/resources/jenkins/plugins/extracolumns/Messages_de.properties
http://jenkins-ci.org/commit/extra-columns-plugin/9d38ff274686255270e08e19d16fc75ce89bd278
Log:
JENKINS-20278 - Added option to use 'pronoun' instead of 'simple name'
to query job type

I committed a first version in the branch "JENKINS-20278".
With Jenkins version below 1.519, only simple name is used to get the job type. This now also includes folders, but not templates (not sure if it's worthwhile to support them below 1.519)!

With Jenkins version 1.519 and higher, users can optionally use pronouns. With pronouns, template names are supported.

I hope this a good compromise, because some people (me included) like the shorter "simple names" instead of the pronouns.

@Daniel: I'd appreciate, if you could give it a try and let me know what you think.

1.532 is not recognized as being >=1.519, so the checkbox is disabled. Maybe because of this?

Manually patching the config.xml produces a result as attached (unchecked and checked job type columns), with template job and template folder with custom pronouns defined. Looks great!

I removed the version check for now. The "Use pronoun" option also works with versions before 1.519, it's just not really useful.