I know it must feel frustrating to not be able to pinpoint that misbehaviour.
Yet I can only state that obviously Pi-hole isn't involved since DNS isn't involved.
Note that your report has not been futile, though.
During investigating your issue, development found a mildly related glitch with dnsmasq that has been reported upstream, and we are also discussing whether we should include that custom option by default (see the beta discussion at "Also forward unqualified host names" creates DNSSEC loop, also for possible unwanted side effects for clients employing DNSSEC in your network).
Still, there isn't much we can do about your client's behaviour, apart from a few speculations outside of Pi-hole's scope.
It could be that your lack of a local domain may be what triggers Windows to disregard DNS resolution.
But then, all your devices should be affected, which doesn't seem to be the case - unless (as Windows name resolution fails to resolve only certain devices) those devices would not support any of the non-DNS means used by Windows.
Hence, would mDNS / avahi be active on those clients?
And revisiting my earlier remarks:
Did you try to configure the single dot as local search domain on that client's network adapter yet?