It's not a contradiction, but redundant insomuch as there can only be one penultimate thing and it is always the final (and first) of its kind.
There can be multiple penultimate things. If you have two quest chains, each one will have a penultimate and an ultimate quest.
But I thought that penultimate meant next to the last, not the last (i.e., final).
That's correct, but it's not a contradiction to say "the final penultimate" thing for the reason that it's not a contradiction to say "the final last" thing. Just redundant.
Though the sibling has a point that there may actually be multiple penultimate things if there isn't a strict ordering between them.