Preventing someone from using mIRC for normal uses isn't very good. You could use a simple on start event if you really wanted to... though, doing so will annoy people.
For a game, just have people login/register using a popup dialog when they join the channel with the bot on it, or have them msg the bot with the login information.
As far as a database, a simple txt file is plenty good enough if it's staying on the bot and not being sent around to others.