Maybe "dedicated" and "infrastructure" are being abstracted into meaninglessness as cloud computing matures.
Its particularly odd with discord, as they clearly mean "instance" not "server".
Sure, it's a chat server daemon (like you could get a web server daemon) - but I think "dedicated private instance" would be better. Should probably drop the misleading bit about "not sharing resources" as I assume instances aren't that isolated?
If I wanted lower latency, I would add WebRTC-based P2P chat for those who support it, to connect directly between servers.
The cheapest dedicated host on AWS costs $370/month: https://aws.amazon.com/ec2/dedicated-hosts/pricing/
So Matrix is misusing cloud terminology when it says "dedicated server."