Dnsmasq is denied right to override unix permissions in /var/log directory. It can work, just /var/log/dnsmasq.log has to be created first with right to write to it. Daemon running network services runs under dnsmasq user, which has no right to write into /var/log.
If you first create file writeable by that user, dnsmasq should be able to write there.
Can you try (as root):
touch /var/log/dnsmasq.log
chgrp dnsmasq /var/log/dnsmasq.log
chmod g+w /var/log/dnsmasq.log
systemctl restart dnsmasq
This should work also with selinux set to enforcing.