@soc describes a workaround to the problem. There is currently no other / better way to get this to work. It needs to be fixed in the future.
Fortunately, this problem has been partially fixed in the current nightly build of the Scala IDE. There is a fix for another issue that disables the Run from Java option: Disable JavaLaunchableTester in Scala files
It does not work for all cases, for example, if a single right-click on a package displays the known Run As options. But for objects with the main method, it works quite well if you use the "Run as" option in the source file.
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