if you want to access vCenter over internet using watchlist, then you need to enable below ports in your firewall to connect with vCenter.
Port – 443, 9443
also from –
You are unable to connect to a VM Console
Watchlist uses web sockets to communicate with vCenter to provide an interactive console after the initial handshake on the following ports:
vCenter 6 or newer: Port 9443
vCenter 5.5u2 to 6: Port 7343
vCenter 5.5: Port 7331
VM console also requires port 902 enabled in firewall.
also instead of directly exposing vCenter to internet I would suggest you to use VPN to connect to your Network and then use watchlist to connect vCenter.