how do you call the linguistic effect of 1 speaker understanding another related language but not vice versa?
Maybe lopsided asymmetric (as opposed to mutual) intelligibility?
Does it mean language A is more ancient than the other?
No, it doesn't. "More ancient" is not a meaningful way to describe languages. All living languages experience drift (random change; possibly at different rates in different historical periods and places), so they diverge. Sometimes, due to geography, politics, wars, etc, the speakers of a given language can end up in multiple isolated groups, and then the way they speak will start to diverge slowly, possibly even borrowing new vocabulary from different sources. It's not right to say one of the resulting languages is more ancient than the other. Rather: they have a common ancestor.
Unfortunately, writing appeared late in human history, and the ability to record sound even more recently, so our horizon (how far back in time we can "look" in order to reconstruct the languages spoken then) is limited. Through comparing multiple related modern languages, linguists can partially reconstruct (i.e. make an informed guess about) what their common ancestor might have sounded like, but beyond ≈6000 years this becomes mere speculation.
Statistically, the bias in intelligibility is more influenced by factors like social prestige, utility in trade, availability of media, literature, and cultural dominance, than by the amount of change accumulated since the two languages diverged.
And, since you said "1 speaker ... another speaker" - it's worth mentioning that the individual experience of those speakers could matter more than the statistical bias.