Hello,
as far as I know (I personally don't use the installers), Alfreso stopped to ship MySQL as an option due to licensing changes following acquisition by Oracle. If you want to use MySQL, you'll have to perform a standard MySQL installation on your own via APT (on Ubuntu) or other means, either before or after installing Alfresco. You don't have to rebuild Alfresco, only change the configuration in alfresco-global.properties to reflect the choice of MySQL, and add the MySQL JDBC driver JAR to the classpath of Tomcat.
Regards
Axel