Okay... good news is, unless your fish gets an infection, he can live a happy life!!
It could have been an infection that made him lose it in the first place, possibly the female betta, poor water quality, other trauma, or supersaturation (gas bubble disease)... since it is missing the globe all together it either fell out OR because it was so severely damaged it could have been reabsorbed into the fish.
Fish do have an amazing ability to heal as long as there is no underlying disease or more trauma. Scar tissue will fill the socket and within a few seeks the orbit will then develop new tissue. It won't look so pretty but your fish should be able to function quite well!!
I would suggest while it just happened recently get some antibiotics in the tank.

Good luck! Let us know how it goes..