Our Remote Target Job answers
http://test.jenkins.retail-sc.com//job/remote-trigger-test-target/api/json

{"actions":[{},{},{}],"description":"Triggered \"remotely\" by <a href=\"../remote-trigger-test-source\">remote-trigger-test-source</a>","displayName":"remote-trigger-test-target","displayNameOrNull":null,"name":"remote-trigger-test-target","url":"https://test.jenkins.retail-sc.com/job/remote-trigger-test-target/","buildable":true,"builds":[],"color":"notbuilt","firstBuild":null,"healthReport":[],"inQueue":false,"keepDependencies":false,"lastBuild":null,"lastCompletedBuild":null,"lastFailedBuild":null,"lastStableBuild":null,"lastSuccessfulBuild":null,"lastUnstableBuild":null,"lastUnsuccessfulBuild":null,"nextBuildNumber":1,"property":[{},{}],"queueItem":null,"concurrentBuild":false,"downstreamProjects":[],"scm":{},"upstreamProjects":[]}

which makes https://github.com/jenkinsci/parameterized-remote-trigger-plugin/commit/d544e329dc27fdf700c5f23191077b4a7074a4d9 decide to be parametrized:

if(response.getJSONArray("actions").size() >= 1)

Like the perform method it needs to be checked if there are parameters inside of the action:
if (!action.has("parameters")) continue;