The official answer page for the Elder Scrolls Online IP address is partially incorrect as of August 2019.correct as of Nov 2022
The correct IP addresses are
PC-EU
159.100.224.0 subnet 255.255.240.0
PC-NA
198.20.208.0 subnet 255.255.248.0
198.20.192.0 subnet 255.255.240.0
For pinging, you can use
- 198.20.200.1 for PC-NA
- 159.100.232.124 for PC-EU
These are the values you should use if you wish to route only ESO traffic to your VPN or to request your ISP to optimize routes
Credits to Mudfish (although I had to do more digging to get the IP ranges)