Here's the scenario, If I block computer A it can still access other clients on the network and other devices on the network can access computer A as well. But computer A cannot access the internet. 
 

I'm curious as to how this works? I was thinking that somehow while computer A is blocked, the default gateway address is temporarily removed from its TCP/IP configuration. Leaving it only with the local LAN IP and subnet mask. Which would allow it to communicate locally to other clients on the LAN/Subnet.

When unblocked, then Computer A would get the default gateway added back onto its TCP/IP configuration and thereby allow it to access the internet.