This may contribute to your observation.
A DHCP client will broadcast for a DHCP server to request a lease from.
Technically, broadcasts are limited to the same link (aka network segment aka collision domain).
Now, certain network equipment like additional routers, APs or switches, as well as VLANs may split your network into multiple separate segments.
If your Pi-hole machine and your Xbox would reside on different links, then your Pi-hole would never receive your Xbox broadcasts.
To verify this, try to connect your Xbox to same segment as your Pi-hole: It should be able to get a lease then.
You would need to configure a DHCP relay forwarding those broadcasts to your Pi-hole on the respective equipment.
Another explanation would be that your Xbox would claim the same IP address for its wired and wireless interface (does it have one?), and would be refused to assign the same IP to the respective other interface.