It's frequently annoying if you've already made the purchase / decided not to, but it's a marketing ROI 'hack' in that the users who are being shown these adverts have already previously expressed some interest in them.
Even if 50% of users aren't interested any more or bought the product, the remaining 50% are still 'well qualified' -- i.e. known relevant -- and so showing the content again to them is more likely to result in sales, and so is 'cheaper' for the advertiser than targeting otherwise-unknown users. It's better for the ad network as well since their customers (the advertisers) will get better results.
Intent mining is really more about analyzing what people are saying online (or, equally, the text they're entering via search engines) and working out what they are intending to do - are they looking to purchase a camera, or are they looking for information about a business?
The two aren't completely separate - remarketing combined with intent mining could presumably have some interesting results (we've seen you were investigating shoes yesterday, and you're travelling to a mall - I'll show you some adverts from shoe stores there), but they're slightly logically different.