Yes I think that people generally have trouble remembering things that bore them, and chores usually pale into insignificance compared to special interests. In my case, if I neglect chores too much then I get scared about descending into squalour, and fear is a strong motivator, so although I often leave chores to the last possible minute, they do eventually get done. At least the most important ones do, but non-urgent chores don't stand a chance. I've often said that my life is like a raft - it never sinks but my feet are always wet.
So NTs, who apparently don't have the burning passion of special interests, don't have quite so much of a problem, though they too have some difficulty with doing all their chores promptly.
ASD also has memory problems of its own. I don't quite know how that expresses itself, but it's typical that we have poor short-term or "working" memory, which could impact on getting chores done.
There's also perfectionism in ASD. For decades I used to fail horribly at tidying up my home because I kept trying to do it perfectly, which was of course impossible, so I got a lot of frustration from it and I found myself unable to continue. These days I try hard to stay mindful of the fact that it doesn't need to be perfect, and I get better results. If my home doesn't get any less tidy, that's a win. If it gets a little bit tidier, that's another win. It just doesn't work to try building Rome in a day.
Paradoxically though, I sometimes make progress by allowing myself to turn a small chore into a mini-special interest - I'll pick a fairly small task and then analyse it very carefully and go for a really good result. It's overkill of course, but at least I find it interesting that way, and I tend to be proud of the result, so I'm more likely to feel like doing it again when it needs re-doing. As it's only a small task in the first place, it doesn't take forever to analyse. And I tend to make it part of the interesting challenge to design the procedure in such a way as to make it take the minimum of time and bother, which again helps motivate me to perform the procedure in the future.
There's also executive dysfunction in ASD. I don't understand that very well, but I wouldn't be surprised if it played a part in forgetting chores. I suppose we've got the start-stop problem going on, for one thing. Once I'm engaged in a thing, it's hard for me to tear away from it, even if it's wearing me out and causing me to neglect other tasks. And I guess many of us have trouble seeing the big picture or overview. In a sense I rarely know what I'm doing because I'm often zoomed in on tiny details, and can't easily keep zooming out to see the context of what I'm doing. So I don't have much of a grip on the overall plan, if I even have an overall plan at all.
Aspies are also said to often have an "out of sight, out of mind" thing going on. Chores are sometimes out of sight. So I bake a loaf and leave it to cool in the kitchen. Next thing I know, it's bedtime, I take my cup into the kitchen and see the loaf, which needs slicing and bagging up before I go to bed. What a surprise! I'd planned to do that an hour or two ago. I guess that kind of thing is one reason I always get to bed later than I'd planned to.