SSO means, you have to login at a single point and having, in the best case, only one source for your credentials. The source is your AD.
Now you imported all your users to alfresco with the ldap sync - your users are known to alfresco now.
In your authentication chain you have configured alfrescoNTLM, which allows you to login with local alfresco users like admin or guest and
ldap-ad which hands over the authentication for all users that are no alfresco internal users to your AD.
That's why you are able to login with your AD users (looks like you are using ldap authentication now).
But like Angel said, you don't have a mechanism that allows to automatically login or enables Alfresco to know that you are already authorized. You need either "NTLM" which enables your Browser to "login" (sends ntlm credentials) to share or Kerberos, that is handling authorization via tickets.
Using NTLM you would have to use (I think) also passthru1assthru in the authentication chain and ntlm.authentication.sso.enable=true and tell Alfresco which server to use for passthru: passthru.authentication.servers=YOUR_AD_SERVER
Also tell your client OS that it is ok use NTLMv1. in Windows:
In addition I can say that when using such technology Active Directory and SSO you can additionally secure the authorization system through adfs sso which in turn makes it possible to set an additional password which is generated using one time security tokens.With this method, adfs authentication acts as a guarantor of 2FA protection.