How to fetch an array in $wpdb?

You have a problem with your query which is you can’t use GROUP BY and ORDER BY before WHERE

replace

FROM tablename GROUP BY submit_time ORDER BY submit_time DESC

with

FROM tablename

This is your query

$results = $wpdb->get_results( 'SELECT DATE_FORMAT(FROM_UNIXTIME(submit_time), "%b %e, %Y  %l:%i %p") AS Submitted,
            MAX(IF(field_name="Name", field_value, NULL )) AS "Name",
            MAX(IF(field_name="Email", field_value, NULL )) AS "Email",
            MAX(IF(field_name="Subject", field_value, NULL )) AS "Position",
            MAX(IF(field_name="Message", field_value, NULL )) AS "Message"
            FROM tablename
            WHERE
            form_name = "Resume"
            GROUP BY submit_time
            ORDER BY submit_time DESC', ARRAY_A);