SKaero I can get you a little further.
If you're using IIS you need to use the non thread safe version of PHP. I was doing testing on Windows 10 Pro x64, IIS, with PHP 7.1 x64 (Non Thread Safe), and MSSQL 2016 Express(ODBC 13).
These PDO drivers work.https://github.com/Microsoft/msphpsql/releases
Place the drivers in your extension directory specified in the php.ini and add the following entries to your php.ini
Then the SQL Server (SQLSRV) will become available and the installer script will flag it as OK, however when testing the config (step 3) I kept getting issue with the roundcube installer script saying that the database was not initialized. throwing an ODBC 13 error I would provide it but I dont actively have it accessible at the moment that I'm writing this. I tried running the database creation (.sql) script directly on the server hoping that would initialize the database appropriately.
As far as SQL is concerned I created a separate user for running roundcube exclusively. Setting both owner and dbcreator permissions for the roundcube database initially. Later in a vain effort to get it working I temporarily granted it sysadmin to no avail as a test.
Then I though perhaps the PDO driver was not working or installed correctly. So i tested it with a small PHP script to connect and return records from a database this worked without issue so it seems to be something particular to roundcubes installer script where it is failing.
One thing i will mention is when i added the extensions at the time i personally only add "extension=php_pdo_sqlsrv_71_nts.dll" however I've done some additional reading and found that its advised to add both as I mentioned above if you try this and find success let me know otherwise I will likely be testing this this weekend myself.