Okay, here is the first character in media that through consuming all the information in the series leads me to think is demisexual. I will explain why in two parts: only developing feelings after forming a strong emotional bond and not showing primary sexual attraction. I decided to go with this one first since I figure everyone at least knows who he is so would be easier to talk about. The first video game character I think of when I think demisexual video game characters is Master Chief Petty Officer Spartan John-117.

First, I'll talk about how John only develops feelings towards people who he has developed strong emotional bonds with. Throughout the lore and history of the universe, Spartans have been shown to still develop feelings and sexual attraction and desires. For example one Spartan II retired from service so she could marry and have a family with a man she fell in love with. There are also cases where Spartans have slept around on shore leave with people they don't even know apart from their appearance. Spartans have also been attracted to other Spartan's appearances. While John has developed deep friendships with some of his fellow Spartans, John has only ever experienced an attraction to two people: fellow Spartan II Linda-058(whom ironically I also suspect is demisexual) and the AI Cortana.
With Linda, this occurred due to them being the best of the Spartan IIs, with John even admitting Linda is probably the best Spartan, thus being put on the same team and sent on missions together. While not as easily seen as with Cortana, during these missions you can tell that he sees Linda as more than a good friend like he does with the other Spartans in Blue Team, including those whom were part of his training team so has known for years longer so should have a deeper connection to them but doesn't. He has also shown to care for her by some of his actions. For example when one of his friends died, he was sad but carried on with the mission. However when Linda was seriously hurt John goes against orders, something he almost never does, to drag her to safety, begging her not to die as he put her in cryosleep to save her until she could receive medical attention.
With Cortana, this is seen visually and heard audibly instead of just read due to Cortana being a main character in the games. As the series progresses, we see and hear John's feelings for Cortana change. In the first game, which is soon after they first met, the relationship is purely professional. In the second game, they are still mostly professional but you can see an emotional connection starting to form. The third game takes that further by them being more personal than professional with each other. Finally in the fourth game is where you see his emotional connection to her form an attraction to her, caring more for her well-being than one would expect from a mere friend, especially considering she is a machine. This comes to a head during Cortana's final moments, where you can hear the pain in John's voice and almost literally see his heart break as Cortana dies. This is a man whose entire life has seen nothing but war and death, and yet the only other time he reacts this way is when he thought he was going to lose Linda. As a comparison, we can look back at Halo 3 when one of John's close friends Sargeant Major Johnson dies. He is sad by the loss, but not nearly to the extent he is in the other examples.
The second reason is his lack of primary sexual attraction, since this sets him apart from being someone who prefers to have an emotional connection before exploring these feelings. As we all know, Cortana took the visage of the silhouetted body of a naked woman. The reason she took this form is explained as most people would react to the attractiveness of her physical appearance, even for a fraction of a second. For an AI, that fraction of a second would be plenty of time to give her the upper hand in the conversation or whatever was going to happen. And yet when she and John first meet, he doesn't react at all to her appearance. He sees her, and continues like it was nothing.