As Azure SQL Data Warehouse does not support recursive CTEs or cursors at this time, you could do this with a good old-fashioned loop, eg:

-- Loop thru Features
DECLARE @counter INT = 1;

-- Insert first record where no parent exists
IF OBJECT_ID('tempdb..#features') IS NOT NULL DROP TABLE #features;

CREATE TABLE #features
WITH
    (
    DISTRIBUTION = HASH ( FeatureId ),
    LOCATION = USER_DB
    )
AS
WITH cte AS
(
SELECT 1 AS xlevel, p.FeatureId, p.ParentId, p.FeatureName, CAST( p.ParentId AS VARCHAR(255) ) AS PathString, 0 AS PathLength
FROM dbo.Features p
WHERE NOT EXISTS 
    (
    SELECT *
    FROM dbo.Features c
    WHERE p.ParentId = c.FeatureId
    )
)
SELECT *
FROM cte;


SELECT 'before' s, * FROM #features ORDER BY FeatureId;

-- Loop recursively through the child records
WHILE EXISTS (
SELECT *
    FROM #features p
        INNER JOIN dbo.features c ON p.FeatureId = c.ParentId
    WHERE p.xlevel = @counter
    )
BEGIN

    -- Insert next level
    INSERT INTO #features ( xlevel, FeatureId, ParentId, FeatureName, PathString, PathLength )
    SELECT @counter + 1 AS xlevel, c.FeatureId, c.ParentId, c.FeatureName, p.PathString + '/' + CAST( c.ParentId AS VARCHAR(255) ) AS PathString, @counter AS PathLength
    FROM #features p
        INNER JOIN dbo.features c ON p.FeatureId = c.ParentId
    WHERE p.xlevel = @counter;

    SET @counter += 1;

    -- Loop safety
    IF @counter > 99
    BEGIN 
        RAISERROR( 'Too many loops!', 16, 1 ) 
        BREAK 
    END;

END


SELECT 'after' s, *  FROM #features ORDER BY FeatureId;

Full code including setup is available here.

My results:

Hope that helps.