Why does not respond to a short name?

Question

linux

There is a router on Arch Linux, dnsmasq configured as dhcp and a caching dns server. In /etc/hosts and /etc/hostname I registered the name "router".
This name does not ping from the Windows machine ("When checking the connection, the router node could not be found").
The ping -a 192.168.0.1 command displays the name router.localdomain; and pings also go to this full name.
But to ping other machines on the network, a short name (for example, server) is enough.
Now I added the following lines to dnsmasq.conf:
expand-hosts
domain=mydomain
Nothing has changed:
ping router - error
ping -a 192.168.0.1 -
router.mydomain
node server.mydomain
Those. for the "third" computer on the network there are pings for the short name for the long one, and to the router - only for the long one (in addition to the ip-address).
On router'e in hosts all machines of a network with full and short names were listed. I tried to remove all nodes from the file, except for the router itself - it did not help.
On a Windows machine, hosts is empty.
On the server machine, there is debian, and now it calmly pings the router and by the short name.
Also, on a Windows machine, after connecting to a working vpn network (Cisco Systems VPN Client) (yes, in general, to any vpn networks), network drives connected using the short name server. Specifying the full name allows you to access the shared resource. After reboot everything is restored.
Tell me, please, is it possible to somehow configure the router or this screw machine so that a short name is enough and vpn does not interfere with short names?

Answer 1

In hosts on Windows (windows/system32/drivers/etc/hosts) added the line
192.168.0.1 router
?

Answer 2

And what DNS servers are registered by the screw machine?