I guess there is a difference between 1st Ed. and 1st run. This is obviously not a first run. Still, the fact that was published in the Egoist may count as a first Ed, so this will count as a new run of the second edition.
There is no denying they are trying to sell more books using technicalities to present this as a "collectors item". But hey, at least it's James Joyce.
There is a difference between a first edition and a first run (usually called a first printing); but this could hardly be a zillionth printing of a booth with the history I described above: a second printing, e.g. uses the same plates as the original printing. What Amazon is advertising is a new edition, and although it may be a first printing of that edition, it still doesn't make it a 1st edn. Why they didn't simply say it was a new edition escapes me.