Those screenshots are from an Asus router. Bucking_Horn is correct:
Most likely the router is also pushing its own IP address for DNS to the clients alongside the DHCP-->DNS setting from the screenshot.
If want to know for sure, install nmap on the Pi-hole host:
sudo apt install nmap
And do a DHCP discovery with below replacing <ROUTER_IP_ADDRESS> with the actual IP:
If output for above one shows multiple DNS servers on the "Domain Name Server" line and one of them isnt Pi-hole, you cant use the Asus router with stock firmware to hand out IP details via DHCP.
I know of below two alternatives options: