How did you configure your Windows client to make use of Pi-hole?
I'm asking because your router is distributing its own IP as DNS server:
*** [ DIAGNOSING ]: Discovering active DHCP servers (takes 10 seconds)
Scanning all your interfaces for DHCP servers
* Received 300 bytes from eth0:192.168.2.1
Offered IP address: 192.168.2.43
DHCP options:
Message type: DHCPOFFER (2)
router: 192.168.2.1
dns-server: 192.168.2.1
Yet your nslookup shows that client to use your Pi-hole at 192.168.2.114, at least for that specific lookup. If you had provided your Windows client with any alternative DNS server in addition to Pi-hole, Windows could by-pass Pi-hole via any such alternative DNS server.
Apart from that, your debug log looks inconspicuous.
So my guess would be that your Windows machine is showing a known misbehaviour where ping would refuse to try resolving a non-dot domain via DNS.
Appending a dot to the name should force ping to use DNS, e.g.
ping node1.
(As a side note, in general, ping isn't adequate to analyse DNS issues, as it is also using other means to resolve a hostname, e.g. mDNS, local hosts file entries, and a Windows ping may also mix in things like lmhosts, NetBIOS resolution, WINS, AD services etc..)