It sounds like you feel about video games the way your parents felt about TV.
Do you watch TV now? Do you get enjoyment out of it even though there are certainly other activities which are more productive? Do you think it would be reasonable to adopt this kind of view over computer games? I think it probably would; no, you don't need to do a 180 and start to love them, but you could accept them as a mindless form of entertainment which is mostly harmless, especially with limits and controls in place. If that feels impossible, then yes perhaps therapy would be useful.
I think at 11, you could be halfway honest with her: State clearly that you don't like video games, and you're not interested in them. You will let her play them under XYZ condition, but you don't really want to talk about them. She can surely talk to friends her own age about them instead. And I don't think it is unreasonable to not want to talk about this when you feel angry, but I also think it would be useful to try and reframe - if she had spent the money on a book subscription instead you'd still be cross but perhaps not feel so betrayed?
I think it might be almost resentment because you don't really want her to have computer games in the first place, so by allowing her to have some you have already been more generous than you feel is reasonable. You feel on some level that she should acknowledge this and be very grateful. Instead, she has childishly and impulsively (because she is a child with immature impulse control, ie perfectly age appropriate mistake) gone against this to procure more.
This feels worse than another kind of misbehaviour, because of the fact you end up feeling "But I've let you do this, which was more than I felt reasonable, and yet you want more??"
Whereas from her perspective, perhaps compared to her friends, she is perhaps very restricted in which games she is allowed; they become shiny forbidden fruit. When presented with a way to access this rarity, she takes it, without thinking through what that could mean.
It is reminiscient of feelings that come up when parents have loose boundaries because they don't want to fight with their children or because they want to be the "fun parent" that says yes all the time - the children get used to exceptions being made constantly, and start to see the exception as being the rule. Then when the parents try to enforce what they think of as the rule, the children are whiny and non-cooperative, which is very triggering for the parent as they feel "But I've given you all this - can't you respect me just this once??"
In that scenario it's because the parents' beliefs (sofas are not for eating on, for example) and their boundaries (oh but go on then just this once every time they are tired) are not aligned/matching. I think you have the same issue. Your actual belief is no video games at all, but your boundary is OK, you can have some. When your DD wants to tip "some" into "more", that is triggering of rage like behaviour and resentment as it feels like she doesn't understand/appreciate what you have already given her in terms of compromosing your beliefs.
In the boundary problem, the fix is to bring the boundaries in line with where the parents' rules/beliefs actually are. In your problem, it sounds like you don't want to do that because you think that would be an unreasonable boundary to hold, so it might be more helpful to try and bring your beliefs in line with the boundary (some video games are OK some of the time).
It is obviously nothing to do with being a single parent, that post was utterly bonkers and unfair.