By default ports below 1024 are privileged and normal applications are not allowed to run on them.
If you search the internet there are loads of conversations about how to do it the right way... well that is too complicated for me, so here's a quick and dirty way to get it set up.
Just run the service using the root user rather than the graylog user - yeah I know, all kinds of a bad idea if this is externally facing, but if it's internal then I think it'll be alright.
In Ubuntu:
sudo vim /etc/graylog/server/server.conf
Change the port number for rest_listen_uri and web_listen_uri to 80
sudo vim /usr/lib/systemd/system/graylog-server.service
Change
User=graylog to User=root
Group=graylog to Group=root
Exit and run
systemctl deamon-reload
to apply the changes you just made