The DNS Manager app is not the DNS Server, in the same way that Firefox isn't Super User.
The DNS Server role included with Windows Server indeed supports recursive queries and being used as a recursive resolver by clients – this is enabled by default, and that's most likely how most people use it, in combination with Active Directory.
Windows' DNS Server supports resolving hostnames both through asking other resolvers ("forwarders") and through directly making iterative queries starting from "root hints".
In other words, if there are any upstream DNS servers listed in the "Forwarders" tab of DNS Manager (not in the network adapter's settings), it'll use those – but if there aren't any, it'll still resolve Internet domains by directly talking to the root nameservers and following delegation chains.
If you want to disable this feature and restrict the server to only answering for locally-hosted zones, check the "Disable recursion" option in the "Advanced" tab.
Regardless of this option, locally hosted zones (i.e. zones that the server is authoritative for) always take priority over recursive lookups, in pretty much any DNS server software you'll find.
