Yes, full duplex means "at the same time each direction" (like a full duplex speakerphone allows you to both talk and listen at the same time without issue).
Thus 1000Gbps, bidirectionally simultaneously (aka "full duplex") is 2Gbps - this is a total speed calculation per line/node, NOT per direction. 100Mbps with full duplex is 200Mbps - 10Mbps with full duplex is 20Mbps, and so on.
If the card is advertised as supporting full duplex at 1Gbps, then it should have settings/code to support the claim - otherwise that is a fraud situation, and should be reported forthwith:
http://www.D-Link.com/products/?sec=1&pid=284
"Additionally, it utilizes auto- negotiation to automatically adjust to the highest supported transfer rate (up to 2Gbps in full duplex mode)."
Clearly, it says it supports 1Gbps full duplex (2Gbps) right there. It isn't ambiguous. Additionally, the Original Poster's screen shot shows 1Gbps.
So why are there not settings in the NIC drivers advanced properties to specifically select 1Gbps half/full mode?
Yes, he/she might be confused as to how full-duplex speeds are (not) shown or indicated in/by Windows. He's never going to see it connected at "2Gbps" by Windows.
But that isn't the issue the the original poster brought up - which is: "why are the SETTINGS for 1Gbps half/full duplex operational mode NOT there in the driver properties?" - a perfectly legit reasonable and obvious question, which, for some reason, the D-Link personnel seem to want to avoid acknowledging or responding to.
The OP doesn't seem to think a "driver update" will make such advanced driver properties "change". I would submit that he/she is wrong - driver updates often change settings/availability of settings for advanced properties of drivers - network interface cards especially. So, he/she would definitely want to install any updated drivers provided by D-Link, both to see if a new advanced options appear, and to simply have the latest "optimized" and "stable" driver scenario.
So, they should install any updated drivers, check the advanced options for 1Gbps half/full modes, if they don't exist, there is nothing lost, and he/she should submit a bug report to D-Link about the missing 1Gbps duplex settings for the driver.