A rich child may end up a rich adult and a poor child a poor adult purely because of nepotism, with the two individuals being roughly the same in terms of skills and abilities.
But another explanation is that the rich child ends up a rich adult because his rich parents actually instill more merit in the child and he ends up with more skills and abilities.
In the latter case the standard could still be meritocratic.
I think there's truth on both sides - things like growing up in an intact family, or learning the value of thrift, are going to inevitably lead to better outcomes for the child - but I think there's also a whole lot of unmeritocratic signaling (who you know, where you went to school, etc) and on the reverse side, measures to prevent people from getting ahead (regressive taxation, poor schools, etc)