Here is the solution...
First, run service control manager (services.msc), find your SQL Server there, and look at properties. Copy service name. In my case, it is MSSQL$SQLEXPRESS.
Then, launch Mail Server UI, stop service, and go to Tools - Utilities - Advanced Settings (Settings.xml), and paste the SQL server name in the SQL Instance box. Save settings.
The SQL server will not appear as a dependency until you reinstall the server though. You can upgrade to the same version, or wait until the next release.
I will also fix dependencies with the Web service module. Apparently, I missed them there altogether.