They hit on the what, just not the why as much. There's only a few things of actual new info I guess: one of the logs is a scientist saying that he believes they didn't even create the giant Marker because they wanted the power, it was because the black Marker/red Marker shards were making them create it. It more or less exists to get people to create more Markers, then each marker tries to gather organic matter to trigger Convergence. The Markers send out a telepathic signal which basically tells other creatures how to create more markers. Another log says average people are driven insane and kill others/themselves, but people with higher cognitive abilities(see: engineers, scientists) are able to keep a fair amount of their sanity and interpret the code that the Marker sends out, which typically is to make more Markers.
Then the rest is from DS1 mostly, where the exception being the Red Marker, whose code more or less just tried to get people to return it to Aegis VII so that it could keep the Hive Mind in check, as it created the Dead Space field that keeps necromorphs from spreading. There is a big discrepancy between DS1 and DS: Aftermath though, as Aftermath shows the Red Marker shard reanimating the dead humans into necromorphs, where DS1 shows it warding off the spread. The Black Marker appears to create and spread necromorphs, the going theory on the Red Marker doing the opposite is just that it was an imperfect copy since they had to use the red material instead of whatever the black one is made of.
The short story is that Markers appear to be sentient, and exert their will on other beings. Different Markers may potentially have different agendas/do slightly different things, but so far all of them at the very least drive people to create more Markers.