Hi Mohamad,
I have recreated the setup as mention below, I could able to ping between VM1 (x network) to VM2 (y Network) without edge/edge cluster.
Here is my topology looks like
ESX1 - Web-VM1 - LS-Web1 ==> Tier 0 <==> LS-Web2 - Web-VM2 - ESX2 ( Ping work without Edge )
ESX1 - Web-VM1 - LS-Web1 ==> Tier 1 <==> LS-Web2 - Web-VM2 - ESX2 ( Ping work without Edge )
I am not sure about your point, In what scenario i need Edge for E-W Communion.
If you want to connect your segments directly to a Tier-0 gateway, then an NSX-T edge cluster is needed for sure as routing between the VMs for their E-W traffic will happen on the Tier-0 gateway which runs on NSX-T edge cluster.