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What does it mean that stocks are “memoryless”?
This is an interesting question that may actually be better suited to Quant.SE. First of all, stock prices are random variables, or, to be more precise, stochastic processes (a time-ordered string of random variables).  The alternative to being stochastic is being deterministic, and I doubt you believe that stock prices are deterministic (meaning, they are fully knowable in advance).  The fact that real world events drive the randomness has no bearing on whether or not it is random.  So, to start, I think you have confused the technical definition of random with a colloquial concept. Now, the heart of the question is whether stock prices are memoryless.  Ultimately, this is an empirical question that has been addressed in many academic studies.  The conclusion of most of this research is that stock prices are "almost" memoryless, in the sense that the distribution of future stock prices displays very little dependence upon past realizations, although a few persistent anomalies remain.  One of the most robust deviations from memorylessness is the increase in the volatility of a stock following large declines.  Another is persistence in volatility.  In general, in fact, the volatility is far more predictable than the mean of stock price changes.  Hence "memorylessness" is a far stronger assumption than the efficient markets hypothesis. The bottom line, however, is that the deviations from memorylessness are relatively small.  As such, despite its limitations, it is a decent working assumption in some contexts.