Le Sphinx appears to have ceased publication shortly after.
On closing date, the receipt of 10 sets was reported, as well as an
extension of time to 1867-12-15.
In April, 1868, the former editor of Le Sphinx, P. Journoud, informs readers that Le Sphinx has ceased publication, and that subscribers will receive Le Philidorien to fill out the remainder of their subscription. In the same issue, the planned publication of the tourney results in the June issue is declared to be postponed to July.
The June issue prints the sets The Last!—The Least? and Gladiator as part of Collection de Problèmes d'Échecs Anciens et Modernes.
No further trace of Sphinx tourney results have been found. The last examined issue of Le Philidorien is issue 6 (Sep. 1868), which appears to be the last published issue.
In 1870, Illustrirte Zeitung prints problem 1 of the set The last!—The Least? under the names of J. Kohtz and C. Kockelkorn, but with no mention that the problem is from the Sphinx tourney. (Illustrated Zeitung, 54/1397 (1870-04-09), p. 274, prb. 1277.) In a reply to a correspondent a couple of weeks later, the tourney is mentioned.
Another few weeks later, problem 2 of Gladiator is printed, this time under the name of Konrad Bayer, in the same manner. (Illustrated Zeitung, 54/1402 (1870-05-14), p. 374, prb. 1287.)
Other problems from the tourney had already been published and/or examined:
The Chess World, 4/34 (July 1868), p. -, prbs. 20-23, and p. 271, prb. 42 prints 4+1 problems said to be prize winners in the Sphinx Tourney. The problems are from the two sets mentioned above, but as there is no indication if or how Chess World obtained official information about prizes, it should be taken with a grain of salt.
Schachzeitung, 23/21-22 (Nov. 1868), p. 353-354, prints some problems by R. Braune. At least problems 2708 and 2711 are from the Sphinx tourney.
Schachzeitung, 24/2 (Feb, 1869), p. 44-57 states that the two sets The Last!---The Least? and Gladiator are by well-known German composers, and prints its own evaluation of the two sets.
Neue Berliner Schachzeitung, 7/1 (Jan. 1870), p. 29, prb. 696-701 prints the set Vive la rive gauche! by L. v. Bilow, said to be one of the Sphinx tourney sets.