The source zip doesn't contain Eclipse project files (.project, .classpath), so it might take a little manual setup to get working. Assuming Eclipse identified the "src" folder as a source folder, you may also need to manually add "i18n" as another source folder. It contains all the localizations for the text in the project (essentially, just stuff in the editor's context menu).
Let me know if you still have problems after doing this!
If you're okay working with the bleeding edge stuff, a better alternative is to download the latest from the project's SVN repository
(installing the Subclipse plugin
for Eclipse if you haven't yet done so). Grabbing them this way, you'll get all Eclipse-related project files, so you should be able to import them directly as Java projects. You'd need to grab the trunk of the "RSyntaxTextArea" sub-project; all the others are add-on libraries or demo projects.