Yes. It is. Also my understanding, and I'm not expert, but it is similar to the blue spotted jawfish and/or catalina goby. I think with cooler waters. Do not hold me to this but I'll need to search my older bookmarks. I thought I read on this on another forum years ago.
my guess is the picture posted by the OP is of a male in breeding/courtship colors, kind of like the pics of tailspot blennies that look super blue and red, when usually they are much more drab. (still think both this species and the tailspot are super cool fish)
edit: a little more research shows the one offered by LA is same genus, dif species:
The caribbean sailfin blenny is a really cool species that's easy to get hold of but even a male on its best day doesn't have such a striking appearance as the gulf blenny. It wouldn't put me of buying one though as they are great character fish.