I assume you are using a physical router?
If you can connect to the Linux VM (on port 8082) from the local LAN (that's what I understood), then - in my opinion - it's got to be an issue with the port forwarding, or another setting on the router. ESXi dosn't block any ports to the VMs.
Its actually (and sadly) the Xfinity Home router. I was delighted to see that they allow you to mess with the port forwarding .. and see it working in most cases.
I want to blame the router but the fact that it works with one VM but not the other is very confusing to me. There are obviously no settings specific to VM or Linux on the Xfinity Router.
I'm happy at least that ESXi does not block ports or have weird firewalls or anything. My only option is to add another router but I would rather not if I can figure this out.