Update: I learned that I can add a ground wire from the ground screw to the wire nut to solve this issue.
True but it won't work if the circuit itself is not grounded.
From just the small portion of the receptacle that you show that is not showing as grounded I see at the bottom that the receptacle seems to be self grounding receptacle. If this is the case then adding a ground wire from the wire nut group of grounds to the receptacle screw will more than likely not give you a ground also.
Do you have a meter to work with. The first thing we need to know is if the circuit (even having a ground wire) is actually grounded.
Look in the box of the receptacle that is showing no ground. Yes, there is a group of ground wires but is any of the wires actually attached to the back of the box with a screw? I am going to say no there is no jumper wire from the group of grounds going to the back of the box which would then ground the box and in turn because you are using a self grounding receptacle would now ground the receptacle. Because the box is more than likely not grounded running a ground wire from the group of grounds to the receptacle will still not ground the receptacle.
You will have to take the ground wire in the box and secure it to the box first but it must also be bundled as it is now so all ground wires are bonded together. Once you do that and install the receptacle since it is a self grounding receptacle the receptacle will now be grounded. Running a ground wire to the receptacle is also ok but just adds another wire to the box.
So first step is the take the ground wire coming in and secure it to the box. Once that is done the box will be grounded but again all ground wires must be bundled together so the ground also goes back out to the next downstream receptacle.
Example of self ground device on a receptacle or switch.
The copper piece under the screw indicates that this receptacle is a self ground receptacle. If a switch had this then the switch would also be considered a self ground switch. But again, if the METAL box that it is mounted to is not grounded this self grounding method will not work. Some people think that because it is called a self ground receptacle that even if the circuit is not grounded that the receptacle will now be grounded anyway. This is not true.
