How do they actually calculate the number of lost coins? Are they just looking at what tx outputs seem to be idle for a very long time or do they have a rationale that they base their argument on?
Pretty much as you said - just coins which haven't been moved in a long time. To say that all coins which haven't been moved in >5 years are lost is wildly inaccurate at best. We see coins which haven't moved in over 5 years being transacted all the time, and we've seen messages being signed from address holding coins which haven't moved in over a decade, proving that they are not lost either.
The only coins which are provably lost and can be subtracted from the maximum supply are those which miners failed to claim in the first place, the 50 coins from the genesis block which cannot be spent, and those sent to OP_RETURN outputs. I am aware of about 130 BTC lost in the first of those categories, and about 27 BTC currently sent to OP_RETURN outputs, meaning the total amount of provably burned bitcoin is only around 200 BTC.
You could relatively safely include all bitcoin sent to obvious burner addresses, but once you start including coins which are inactive or you think belong to Satoshi, then your estimates become increasingly inaccurate.
That is exactly what I thought. Just from the stories that you hear here and there, the probability that the lost coins are in the very low millions is relatively high. I remember a story of a guy who lost 70,000 on a hard drive I think, and another with 30,000. So even while this is wild speculation, it is likely that people did indeed throw away hard drives with Bitcoin on them. Then again you can't even verify if these guys just wanted a nice article in the newspaper about them.
But if you think about those losing Bitcoin, it is hard to conceive of the circumstances how that could have happened. If someone is literate enough to set up mining operations during Bitcoin's early days, those people probably knew relatively early on that there was a market for Bitcoin. Why would someone just throw a hard drive out the window with Bitcoin on there? I don't know.
But I fully agree with what you said in regards to coins not being moved >5 years are most likely lost. That is certainly nonsense.