When executing the TestLink Jenkins job, Jenkins monitors the successfull execution of the job regardless of what the job may be. Imagine some kind of test automation with hundreds of test cases is run. Jenkins would display this job as successfull even if some test cases of the automation failed. The failed test results can only be observed in TestLink.
In a big project there may be several Jenkins jobs (build the software for different platforms, execution of automated test suites,...) and it may be helpful for the Jenkins responsible to see on the Jenkins page if everything worked out fine.
So the request is to be able to display a Jenkins test automation job as "failed" if at least one test case was not executed successfully. The detailed results remain in TestLink, of course.

In my opinion it doesn't matter if the job was not executed successfully (e.g. because the automation software could not connect to the target) or if the job ran successfully and one of the test cases failed. In both cases you need to check what went wrong and therefore a "failed" indication of the job is ok.