Patrick,
Rules issues aside, there are multiple descriptions (and photos) of the hole, and it played straight up a cliff with the green on top. Here is Horace Hutchinson, again, describing the hole in 1903 in Pearson's Magazine:
A little further on in the present Biarritz course there is a hazard of unusual nature. This is a cliff face opposing you, up which you have to loft the ball sixty odd feet in the air, with a full mashie shot, or something of that kind. There are many Biarritz golfers who have played there steadily yet never have ascended that giddy height—that is, never have persuaded their golf ball to mount it—and it is certain there are many who never will.
Turning to the rules issue . . . In The Happy Golfer (1914), Henry Leach also described the hole and directly addressed your rules question, Patrick. Note that at this time, No. 8 played down into the Chambre and No. 13 was the "Cliff Hole" out of the Chambre. (This might explain the sign on the tee box in the photo (if it is indeed a "13.")
The ascent to the higher surface has to be made at the thirteenth, and it is done at what is known to every one as the Cliff hole.
Nearly all who have never even seen it have heard of the Cliff hole of Biarritz, have studied pictures of it, and speculated upon its peculiar difficulties. No hole on the continent of Europe has nearly such a reputation; indeed, it is perhaps the only one with a special celebrity. I have been asked questions about it in America. I have seen and played it, examined it thoroughly, and thought it out. It is a queer thing, quite different from any other hole I know. It needs such a shot to play it properly as is not demanded elsewhere. And yet it requires absolute skill, the proper shot must be played and played thoroughly well, and it is practically impossible to fluke it. Why, then, should this not be reckoned a good golfing hole? The circumstances are these: The teeing ground is on the lower level, and it is only some fifty yards from the base of the cliff. The ground in between is rough and stony. The cliff here is about forty yards in height, and, if not vertical in the face, bulges outwards frowningly at the top, while a thin stream of water trickling down at one side seems to add a little more to the fearsomeness of the thing. At the top edge of the cliff there is grassy ground sloping quickly upwards for about a dozen yards until a line of wire is reached, and there the green begins. The fact that the green (which is tolerably large and in two parts, an upper and a lower) then slopes downwards away from the player does not make matters easier. Beyond it is another precipice, but wire netting is there to save the ball from this, and there is some wooden palisading to keep it out of trouble on the left. Then there is a local rule saying that if the ball reaches the top of the cliff, but does not pass the wire, it must be teed again, with loss of distance only, the man not being allowed to play it from the tee side of the wire. (He would do so at peril of toppling over the cliff!) But all these things do not make this awful hole much easier in the play. One day I sat on the edge of the cliff and watched the people playing it, and the ball that reached the green and stayed there was a rarity. It can be done. Braid and Taylor and Vardon would do it all the time, and it is no trick shot that is wanted. You might hit hard at the ground in front of the wire and make the ball trickle on, but that would call for more than human accuracy. Or you might sky your ball up to the heavens and let it fall straight down on to the green, and that would be superb. But champion Taylor would take his mashie and play, perhaps, some fifteen yards above the cliff with all the cut that he could put upon the ball, and then he would be putting for a two. A difficult hole follows, but after that the work is easier.