self-imposed chastity and aversion to physical contact do not meet the definition of asexuality. If a person has any sexual attraction to others, that person cannot be accurately described as asexual.
Here we go again into the murky depths of language and implied meanings. The above definition is certainly correct.
However, without being a mind reader, from what I read and understood, it seemed to me that, what some people at least, understand under asexuality, means - for them - going without physical sex, or not committing any sexual acts with others, maybe not even masturbating, though that last isn't clear from what I've read so far.
I suppose some clarification might be useful
You could also ask, which I actually do right now, what word should be used to describe someone who refrains from sexual acts, but still has a strong sexual imagination? To others, such a person might appear to be chaste, but they are certainly not so in the mind and may even be more obsessed with sex than 'normal' people.
Surely there can be little choice between a self-imposed state of frustration and actually fulfilling a desire.
I don't think the use of self-imposed 'frustration' is an accurate word. There is nothing 'frustrating' about self-imposed periods of abstinence, if abstaining provides a different sort of sexual pleasure. Granted, the pleasure is mental, imagined and in the mind, but that doesn't mean it is any less intense, sufficient or fulfilling for some people. This isn't for everybody of course, but apparently some people do find a certain type of fulfillment. Just think of religious or monastic orders throughout the ages. In the distant past, just as now, people often struggled with their sexuality, it sometimes being in opposition to religious beliefs. And this not only in many forms of Christianity. It appears in the Classical Roman-Hellenic world as well, where abstinence could at times end up being transformed into a form of mental ecstasy or transcendental pleasure of the mind.
As a personal observation, due to circumstances, I have gone for very long periods of physical abstinence (and not just a few days or weeks or more) and I know from experience that being in an acute state of mental sexual arousal without physical fulfillment, can be especially overpowering and intense, infusing almost everything with sexual connotations and reference. The smallest occurrence or sight can provoke strong and wondrous streams of sexual energy into the imagination.
This is, of course, not a life-long option to ever choose as life-style, not in my opinion for whatever that counts, but there is an attraction to it, if you have the discipline to adhere from physical contact with others.