May be this is the "corrected" article.
There is so much disinformation out there with many people making a mountain out of a molehill. The actual ruling has not been posted on the court web site, so the conflicting stories can not be sorted out.
Missouri appealed a stay of the execution, which was set to expire anyway this afternoon. Earlier today, the court ruled 9-0 to NOT lift that stay, which then ended on its own on the original schedule.
Meanwhile, the convict had two appeals working up through the courts for a stay of execution for other reasons. In the first, he claimed his death sentence was racist. The court WITHOUT alito ruled 8-0 NOT to grant the stay.
In the second, he claimed that lethal injection was cruel and unusual punishment. Alito heard that request, and then the court voted 5-4 to UPHOLD that request, thus putting the execution on hold.
So, there were THREE votes today, one on a Missouri request (denied 8-0), one on a convict request to stay based on racism (denied 9-0), and one on the convict request to stay based on 8th amendment (accepted 5-4).
Apparently the court has a couple of these 8th amendment appeals about lethal injections wending their way, and I guess Alito thinks it's worth hearing the argument (or at least letting a lower court decide whether to hear the argument).
Anyway, I hope this clears up the confusion.