Vertica UNION and ORDER BY
The query needs ORDER BY in the end, not in the subqueries (and note that the parentheses are optional there, at least in standard SQL, not sure if Vertica requires them):

( SELECT country_id, country_name 
  FROM country_dim 
  WHERE iso_country_code LIKE 'US')
UNION 
( SELECT country_id, country_name 
  FROM country_dim 
  WHERE iso_country_code NOT LIKE 'US')     -- without ORDER BY
ORDER BY 
    CASE WHEN iso_country_code LIKE 'US' THEN 0 ELSE 1 END ASC,
    country_name ASC ; 


But since you are grabbing all the data from the same table, there is no need for the UNION and the subqueries:

SELECT country_id, country_name 
FROM country_dim 
ORDER BY 
    CASE WHEN iso_country_code LIKE 'US' THEN 0 ELSE 1 END ASC,
    country_name ASC ;