If you want to get rid of the registration dialog, just register. Send 50 SEK + 10 SEK for snail-mail-shipping to get a key to remove the shareware message. Include your exact name, a reply address and the version number 1.0. If your reply address is an e-mail address you don't have to pay the additional 10 SEK for snail-mail. If you want me to mail you a floppy I have to ask for extra 40 SEK. I can also accept payment in USD. Add 5% extra for exchange fee. Don't send cheques since banks charge too much for cashing them in.
When you register you get the key which removes the registration dialog. Some locked features (cannot play more than one round, cannot save or open a savefile) are enabled as well. The key will also unlock future versions of Mah Jong (alt you may order a new key for the next version without any cost except for snail-mail if you don't have e-mail).