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The script is missing a left join to sys.types to grab table type information, which also requires execute permissions to use (alternatively join sys.table_types, you'll get the same data). Try the following:

SELECT  DB_NAME() AS 'DBName' ,
        p.[name] AS 'PrincipalName' ,
        p.[type_desc] AS 'PrincipalType' ,
        p2.[name] AS 'GrantedBy' ,
        dbp.[permission_name] ,
        dbp.[state_desc] ,
        COALESCE(so.[name], t.name) AS 'ObjectName' ,
        COALESCE(so.[type_desc], N'TABLE_TYPE') AS 'ObjectType'
FROM    [sys].[database_permissions] dbp
        LEFT JOIN [sys].[all_objects] so ON dbp.[major_id] = so.[object_id]
        LEFT JOIN [sys].[database_principals] p ON dbp.[grantee_principal_id] = p.[principal_id]
        LEFT JOIN [sys].[database_principals] p2 ON dbp.[grantor_principal_id] = p2.[principal_id]
        LEFT JOIN [sys].[types] t ON dbp.major_id = t.user_type_id
WHERE   p.[name] = 'db_executor';