This is the key line. This is the only type of cherry picking they are referring to: you run the experiment until the results look favorable and then you stop.
With a frequentist analysis the p-value depends on why you stopped, because that changes the reference set that the outcome is calibrated against (the set of outcomes that are considered as-or-more-extreme). This is illustrated by the example of flipping a coin and getting HHHHHT at the beginning. If the experiment was "flip a coin 6 times and then stop", then HTHHHH is as extreme as HHHHHT. But if the experiment was "flip a coin until you get tails" then HTHHHH isn't a possible outcome (because you would have stopped at HT), so it's not in the as-or-more-extreme set.
This is often used by Bayesians as an argument against frequentist statistics. Personally I've never found it very compelling, since (1) the effect tends to disappear as sample sizes grow (due to likelihoods approaching normal distributions in the limit under weak conditions) and (2) experiments generally have a predetermined stopping condition and I don't particularly care what the analysis would have been if the stopping condition had been defined differently. It is however a philosophical point in favor of Bayesian analysis.
Yudkowsky then presents this as a counterargument from the frequentist character:
> Scientist: Okay, that last claim in particular strikes me as very suspicious. What happens if I want to persuade you that a coin is biased towards heads, so I keep flipping it until I randomly get to a point where there's a predominance of heads, and then choose to stop?
Basically, "OK, if the stopping rule doesn't matter for Bayesians, what prevents me from using the stopping rule to manipulate the experiment by choosing to stop when the evidence looks favorable?"
I consider this a bit of a straw man because I've never heard a frequentist actually use this argument. I have heard Bayesians present it as a frequentist argument many times. But probably at some point in the past one or more frequentists did use this as an argument.
The Bayesian response is "You can try, but you probably won't be able to get very strong evidence in favor of a false hypothesis." Which is true and fine, as long as all the data are fully and fairly presented. But it doesn't prevent me from accumulating data over multiple attempts (by selectively failing to report attempts that don't turn out well): it's unlikely that I'll be able to get a 20:1 likelihood ratio against a true hypothesis in a single run (this is what the discussion about python programs is about), but it's not hard to get say 2:1 likelyhood ratio against a true hypothesis in a single run, and then do that several times, discarding runs that don't work out for me.
Yudkowsky's analysis doesn't address this. He assumes throughout that the data are all fully and fairly presented; I'm not throwing out any data from days when it didn't work out in my favor or anything like that. He also (as I pointed out in another comment, and as levocardia illustrated wonderfully in yet another top level comment) ignores the many other ways of manipulating outcomes other than just deciding when to stop collecting data: choosing which variables to include/exclude, choosing to analyze only a subpopulation, choosing transformations to apply to variables, and many more choices that a data analyst can make to obtain more favorable results. Bayesian analysis is not immune to any of these other manipulations.