If you've been given a virtual ethernet cable then just treat it as if it was a real ethernet cable. There's a few protocols that may be stripped (but may not be - I've had both) -- lldp, LACP, etc, but the beauty of a layer 2 link is you can simply treat it as a 100km ethernet cable.
The Tier-1 ISP themselves may be using something like VPLS to provision you the circuit, but you don't need to worry about that as the customer. Plug it in and you should be able to ping 126.96.36.199 from 188.8.131.52 and 184.108.40.206. You should hopefully see City B appearing in the "ip neighbours" list on the core router.
When you run "ping 220.127.116.11" from 18.104.22.168, the first thing that will happen is that an ARP message will be sent out by City A's router on the core router interface - basically "who has 22.214.171.124". Assuming the core router has ports 2, 3 and 4 bridged, this arp will be sent to the radius server and city B. City B will respond "I do, my mac address is xx:xx:xx:xx:xx:xx", and then that will be installed in city A's arp table, and any traffic going to 126.96.36.199 will be sent to that mac address. The router knows that the mac address is on port 3, and forwards it off to city B.
Once you've got pings working, confirm that your MTU is 1500 bytes (do a ping with a size of 1500 bytes and dont fragment set).