Do you have to bye a new game to make another account on wow

The account you have (as well as a new one) is created on the Battle.net server based on an authentication key. It does not matter whether you get the key from a CD package or you buy a download version, but to get a second account you must buy another game.

If you wish for a second account, it may well pay to use the recruit-a-friend option from your first account to effectively recruit yourself, and upgrade that account to a full account instead of a trial. That way you also gain the X-52 Nether Rocket mount.