It's not just a "transcription" it's people taking their own interpretation of the dialogue and translating it however they see fit. Some people leave in puns, some people take them out, some people add a note at the top of the screen to explain the cultural significance of a certain line.

Actually, that's explicitly allowed by copyright law (EDIT: so long as you're in the accessibility business): http://www.copyright.gov/title17/92chap1.html#121

(Granted, that the "phonorecord" must be in a "specialized format exclusively for use by blind" is fuzzy.)

It seems to say that "it is not an infringement of copyright for an _authorized entity_ to reproduce..."

Ah good catch. From the definitions:

“authorized entity” means a nonprofit organization or a governmental agency that has a primary mission to provide specialized services relating to training, education, or adaptive reading or information access needs of blind or other persons with disabilities;

Sounds like the exact same website could be setup and remain the right side of the legal boundary simply by presenting themselves as a service for the deaf. YMMV.

The owners would have plausible deniability I feel, they don't know whether their users are deaf. Then it would be down to the copyright owners to address whether individual users had rights to format-shift audio tracks [they purchased] in to a format they could consume [specific language subtitles].