You did misunderstand the attack. The faked packages aren't send to the client. They are sent to the server with the address of the client you want to dos as the sender. The goal of this attack is to make the server believe that the address is available again. This will only work if you prevent the real client from communicating with that server.
You can find a documentation of how this is best done here.
// When a Host obtains a DHCP lease there come some limits with it. The lease has a lifetime after which it expires if it isn't extended. But there is also an additional time limit which is called renewal time which is the time limit after which the client should talk to the DHCP server again to extend the lease. Many operattion systems even renew their lease more often than imlied by the renewal time.
When you now start portstealing your target and send a RELEASE Packet to the DHCP server the server will mark the lease as available again. You then start aquireing this lease with a fake mac address using DHCPig. When the targeted client then talks to the DHCP Server to renew his lease the server will send a NACK packet which will prevent the lease from beeing extended at least and might cause the client to discard his configuration.