....
This is misleading. There was other testimony and evidence against him. You may not believe it was strong evidence, but there was a case presented that went beyond the accusation of the other murderer. Also, if not showing the interview to jurors was a material flaw, was it raised on appeal?
Sneed (the accuser) did testify and was cross examined. The jury found him credible. This is part of their job. I assume (but do not know) that the "you are just ratting him out to get a lower sentence" defense was raised and rejected by the jury. Again, part of their job.
The bare bones of the case can be read here:
http://www.ca10.uscourts.gov/opinions/10/10-6244.pdf
It covers some of the other evidence against Glossip.