When I log in to Jenkins, I can see the "Query and Trigger Gerrit Patches" on the left side of the screen.
However, other people cannot see this useful option.

The "Query and Trigger Gerrit Patches" option is only available to Jenkins administrators. 

See:  https://github.com/jenkinsci/gerrit-trigger-plugin/blob/master/src/main/java/com/sonyericsson/hudson/plugins/gerrit/trigger/PluginImpl.java#L91

If would be better if this did not require such high privileges.

Note that I am using the Role Strategy plugin.