Isn't it a selinux policy that need to be set ? https://access.redhat.com/documentation/en-us/red_hat_enterprise_linux/7/html-single/load_balancer_administration/index#install_haproxy_example1 ?
Who configured haproxy to listen on 8081? Was it a customization (see #2 above in comment 6 ) or out of the box?