Just some clarification, because some terms are being mixed here.
SQL Compact is different from SQL Express. SQL Express is a version of SQL server (the free version)
To really check what your old installation is using, I'd recommend checking Configuration\Database Tables.
If you are using SQL Express, I think you might still have an SQL Compact Database in your installation folder from a previous move.
If you want to move from SQL Express to SQL Server, you should follow these instructions: https://www.lansweeper.com/kb/170/moving-your-database-to-a-different-server.html
If you have verified that you are indeed using SQL Compact then the original linked article should work.