The autoflight system is indeed typically engaged shortly after takeoff.
However in the particular type involved cannot perform autolands off a non-precision or RNAV approach. At some point, usually around 400' on most approaches, even if one has used the ILS in the initial phase of the approach, someone has to hand-fly to the landing.
Without a link to the original story, the comment, "these aircraft basically land themselves", isn't worth quoting and isn't worth giving credence to.