For all Chivalry 2 players who are trying to join the party need to allow edge traversal in their chivalry 2 firewall rules.
How to Fix Party Invites Not Working
Start > firewall.cpl > Advanced settings > Inbound Rules > Chivalry 2 > Properties > Advanced > Allow Edge Traversal
There should be 2 inbound rules for chivalry 2. One for UDP and the other for TCP.