You are invoking the method printIfArtifactVersionDirectory for all visited directories. I did a little change to make it obvious:

static void printIfArtifactVersionDirectory(Path path) {
    System.out.println("--- " + path);
    ...
}

With that additional output you will get:

--- C:\Projects\stuff
--- C:\Projects\stuff\org
--- C:\Projects\stuff\org\foo
--- C:\Projects\stuff\org\foo\bar
--- C:\Projects\stuff\org\foo\bar\1.2.3
C:\Projects\stuff\org\foo\bar
--- C:\Projects\stuff\org\foo\bar\1.2.4
C:\Projects\stuff\org\foo\bar
--- C:\Projects\stuff\org\foo\bar\blah
--- C:\Projects\stuff\org\foo\bar\blah\2.1
C:\Projects\stuff\org\foo\bar\blah
--- C:\Projects\stuff\org\foo\bar\blah\2.2
C:\Projects\stuff\org\foo\bar\blah

So you get the output as often as you have artifact version directories. If you want to remember that you already did the output for one directory, you must make store this information somewhere. One quick implementation could be:

static class Foo {
    private static final Set<Path> visited = new HashSet<>();

    static void printIfArtifactVersionDirectory(Path path) {
        ...
        Path parent = path.getParent();
        if (!filePaths.isEmpty() && !visited.contains(parent)) {
            visited.add(parent);
            System.out.println(parent);
        }
    }
}

With this you get the expected output:

C:\Projects\stuff\org\foo\bar
C:\Projects\stuff\org\foo\bar\blah

A better solution would be to use the set for storing the visited parents and only print them after visiting them all:

static class PathStore {
    private final Set<Path> store = new HashSet<>();

    void visit(Path path) {
        File f = path.toAbsolutePath().toFile();
        List<String> filePaths = Arrays.asList(f.list(new MyExtFilenameFilter()));
        if (!filePaths.isEmpty()) {
            store.add(path.getParent());
        }
    }

    void print() {
        store.forEach(System.out::println);
    }
}

Usage:

PathStore pathStore = new PathStore();
Files.walk(Paths.get("/path/to/stuff/"))
        .filter(Files::isDirectory)
        .forEach(pathStore::visit);
pathStore.print();

You can use the try with resources if you don't use a separate method for getStream() :

public List<String> getList(Path dir) {
    if ( Files.exists(dir)) {
        try (Stream<Path> stream = Files.walk(dir, 1)) {
            return stream
                    .filter(Files::isRegularFile)
                    .map(dir::relativize).map(filename -> filename.toString())
                    .collect(Collectors.toList());
        } catch ( IOException ioe) {
            System.out.println("ERROR: " + ioe.getMessage());
        }
    }
    return null;
}

The try-with resources closes the Stream as soon as the try-with-resources block is done, which is causing your issue.

In the above example, all remains within the try-with-resources block, so the Stream can still be used to find the List you want.