Maybe an usual and non-native wording, but I take it to mean "not that old but a little more than the sufficient level of oldness to qualify".

It's pretty obvious that it narrows the statement of "old enough" to be a fine-grained distinctions fitting, in this case, to a short timespan, possibly a few years, that some readers may consider to be old and others not old at all.

Is there some other meaning you had in mind when asking this, or was this a pedantic question?