Accessing WPDB Multidimensional JSON Array w/ Javascript

Looks like you want to use something like result = $.parseJSON(data). Then you can access the data with result.win_id, for example.

As an aside, you should sanitize the input to that database query using prepare with something like:

$wpdb->get_results( $wpdb->prepare( "SELECT * FROM wp_winners WHERE user_id=%d", $user_id ) );