I don't have a clue about "abyss server". The easiest way to get wp going on your local box is to get XAMPP from apachefriends.org. It comes ready to use with apache, php and mysql, all talking to each other and happy. Once you've installed that on your box, THEN install wp.
[Edit: *sigh* Answer the question, idiot....]
Yes - you do have to have mysql.... the only way I know to get it running right is to use XAMPP. There are probably a lot of other ways to get it working, maybe someone else will know without going the Apache/XAMPP route.