I don't really understand the confusion. The OP is extremely thorough (if you read it all) and I've never heard of this, but it seems very clear to me:
*asexual - no interest in sex; no direct sexual attraction or ability to be turned on by someone's appearance; no secondary sexual attraction based on emotional bonds; this does not mean sex is physically unpleasant to them per se, but they have no real sex drive to speak of.
*demi-sexual - no interest in sex through primary attraction but does experience sexual attraction only when a deep bond has been formed (this does not merely mean they wait to make a romantic move or wait to have sex, but that the attraction actually never occurs to them prior; and it's not in one case, like "I never saw you that way" but "that way" never existed before)
*sexual (for lack of a better term) - interested in sex, with a sex drive somewhere in the average spectrum, and capable of both primary attraction (being turned on by someone physically or who has obvious qualities that are attractive, before a deep bond is formed) and secondary attraction (being sexually interested someone with whom you have a deep bond with)
Perhaps - If there are people not who just fear emotional bonds and avoid commitment but actually lose sexual attraction whenever they form a deep bond, that may be a forth dimension of sexuality.
I agree that I don't think this spectrum is quite the same as homosexuality/heterosexuality spectrum, just because it's not going to have a societal impact and thus any related discrimination will likely be fairly rare and/or personal, rather than systematic. But as to writing a character (the point of this thread), it could be an interesting spectrum to consider.
I'm sure some of the existing romance options need to be romantically involved with the Inquisitor before taking a roll in the hay. That has been the case with every DA game so far. With that in mind it seems what is really being asked is for some of those potential LIs to self-identity as demisexual as well. While I'm okay with real people self-identifying however they like, I don't think any characters in the game should describe themselves as demisexual.
I'm not seeing a distinction between people who self-identify as demisexual and people who are either attracted to the opposite or same sex (or both), who just don't take sex lightly. Also the term was invented in the internet age by a 15 year old girl on a roleplay forum. It would be out of place in DA dialogue, in my opinion.
FTR, I don't think the OP needed the LI to use the word demi-sexual. Nor would a portrayal necessarily do that. I can't recall either game ever using the word bisexual either, frankly. Maybe this one will, or pan-sexual, but it's more likely characters won't be walking around saying, "I'm a pansexual" (I don't mind if they do, unless it's bad writing) and instead will just be a pansexual.
The case for Merrill as demi-sexual can certainly be made, based on OP's parameters, but it's not about "not taking sex lightly." That's a value system, not a function of attraction. I don't think you can consider any other LI demi-sexual.