does not list choiceParam, although that parameter exists and works.
choiceParam is provided by the Dynamic DSL which is not available in the (static) API viewer. See the link for details.
I think there is still a bug here. There is a non-dynamic version of choiceParam (https://github.com/jenkinsci/job-dsl-plugin/blob/job-dsl-1.74/job-dsl-core/src/main/groovy/javaposse/jobdsl/dsl/helpers/BuildParametersContext.groovy#L86), and that one is not visible in the API viewer.
Compare it with, for example, booleanParam, for which both dynamic and non-dynamic versions are shown.
Roman Donchenko yes, you are right. https://github.com/jenkinsci/job-dsl-plugin/pull/1188