My bad. It turns out that it is very easily possible to export test cases with test steps:
- Choose Test Reports in the topmost menu of Testlink.
- On the Reports and Metrics page, select OpenOffice Writer (or MS Word) as the Report Format.
- On the left side, select Test Plan Report. On the right side, select the checkbox Test Scenario (you don't need Test Summary or any other options). Below, click on the test case folder that you wish to export.
- You get the document for download. (Note: may require some formatting.)
Alternatively, it is possible to choose HTML in step 2 as the report format and save the frame.
While it is possible to select OpenOffice Calc/MS Excel, there doesn't seem to be a way to include test case steps.