The lobby server runs on an instance at
DigitalOcean. The game server is of course created by the client hosting a match (similar to how you would do it under Unity network).
I wrote about the lobby server
here.
I should probably look into putting some kind of monitor software onto the lobby server to at least see how many connections there are on it and what the load is like. Atm I'm simply using the $5 option but I guess it should be enough for a small game like this.