Pretty much yes, not sure why you’d need your own router then.
The strange part from my perspective is when you say “uni” and “modem” in the same sentence (I’m imagining small racks with a bunch of RJ45 and fiber going out the building). Have you physically seen the devices/equipment that provides you with internet - are you sure you’re asking for the right thing?
[caveats and disclaimers aside, in rough strokes:]
Connecting your computer directly to the internet, is relatively secure these days.
It is the same, or as secure, as connecting your computer to the internet behind a NAT firewall/gateway and then punching a big hole in that firewall using DMZ forwarding to let internet in, while still allowing your computer to go everywhere else on the internet as it pleases.
Replacing DMZ, with UPNP (or nat-pmp - slightly better) is about the same thing security wise.
In terminology used by various IT security courses a DMZ is a firewall setup where you’d take your game server and put it on its own network and isolate it to only allow the minimum of incoming connections required for the service it needs to run. e.g. it doesn’t need to make outgoing connections to the internet, so that’s closed off. The idea is that once there’s an unpatched bug in the game server, the attacker/malware can of course take over the game server, but that’ll be useless to them… Once you notice that’s happened rest of your compute resources are still unharmed, and it’s not like that machine has caused further damage, you’re free to nuke the game server from orbit and restore it from a backup.
If this is something you’re proposing to do, then having a separate firewall that the machine is not allowed to easily access would be useful, as you could use it to prevent game server from going onto the internet, or from being used to spread malware further on your LAN. Is this what you were proposing?