I guess the idea is that the theory of algebraically closed fields can't do anything to distinguish or relate algebraically independent transcendentals,
which means if we have two extensions of 𝐐 with their respective transcendence bases having the same cardinality, ANY bijection at all between those bases can be extended into a field isomorphism,
... and if it so happens there's no way to have such an isomorphism respect convergence of sequences (i.e., f(lim xₙ)=lim f(xₙ)) w.r.t. ANY of the metrics, we just don't care.
Seems like something they ought to have known about in 1982.
OTOH it's a completely useless isomorphism, so maybe it just wasn't worth mentioning.