I'd do what everyone else said:
1) Turn off power, remove outlet, cap and tape wire.
2) Score wall (3/4" through) to prevent damage to sheetrock
+ 3) Score equal amount of sheetrock off the bar to possibly reuse on the hole in the wall
+ 4) Break away sheetrock and pull wire back carefully to the wall
5) Sledge/kick sheetrock to expose insides
+ 6) disconnect bolts/other fasteners to floor and wall
7) Finish removing
+8) Do the same thing for the bump out next to the door as well behind the bar area. Almost certain that cannot be load bearing and will just be in the way probably. It was meant as a "surround' for the bar area.
For wiring (if you're not handy with electrical):
- Reuse the electrical box from the bar in the wall where you removed it from.
- string the wire through it and attach the wire within 6" of the box (code) on the stud with a plastic+nail staple, centered in the stud (~1 3/8" from front and back edges)
- Pull wire through the box and leave at least 6" extended from the box (again, code)
- Turn off power, cut wires, peel back Romex white shield and from the individual wires and reconnect to outlet that was in bar.
(Black = hot and goes to brass colored screw post -- short side on outlet slot, White = neutral and goes to nickel colored screw post -- long side on outlet slot, bare copper goes to green colored angled post attached to main metal mounting tabs of outlet)
- Mount and put faceplate on.
- Turn back on power and test.
Note: Even though you have another outlet to the left very close, my guess is they ran the power to the bar from the right then back out to the out to the left (or vise versa). In any case, once that wire is clipped there you will not be able to simply connect it and hide it in the wall. You'll need a junction box at the very least, and at that point you may as well just put the outlet in the hole you'll be left with anyway. (You are not allowed hidden junctions behind wallboard or ceilings per code). You may be lucky and the bar outlet was the last one in the run coming from the left, in which case you could just remove the wire from the outlet to the left if you didn't want to move it onto the wall so close for the extra one.
BTW what's with the uber-thick wall ? The core wall looks standard 3.5" but it looks like another 5.5" from the frame of the window which too looks recessed from the outside so I assume that's flush with the concrete of the basement already? Why is that interior wall built so far away from the foundation? Seems really strange.