You can always "comment out" (#) or delete these changes if they don't work.
Use sudo -e /etc/network/interfaces (or if you'd prefer a graphical editor: gksudo gedit /etc/network/interfaces) to make the file look:
The last two lines are probably unnecessary - so they're commented out already. With only the one machine on the network, you probably won't need the gateway or DNS server. Save the changes and restart or reboot (I prefer a reboot to re-sync networking and NM).
iface lo inet loopback
iface eth0 inet static
One caveat I just realized - if wireless is also using the 192.168.2.0 network, this may not work. Two interfaces in the same subnet plays havoc with routing... But, you could change the wired addresses on both machines to a different subnet - say... 192.168.3.0