It is a user authentication/privilege problem.
Did you read this FAQ item:
http://www.webyog.com/faq/23_18_en.html ?
I have sync'ed often between two PC's on a LAN with a router as DHCP server. No problems in that. Type of (physical) network does not matter either.
I believe in your case the problem that ROOT is only allowed to connect from 'localhost'. If not that is it, I don't understand you perfectly and I shall then ask you to explain a little more detailed (we love screenshots!)
You could install SQLyog on PC2005 too and change the root's hosts' access from 'localhost' to '%' or just '192.168.0.%' (in case you only want to connect from your LAN).
If you connect on port 3306 it is irrelevant if there is a webserver installed. But of course you will need it for HTTP-tunnelling. But not much use of that on a LAN!