Yes, it is clear in the audio, requested and cleared for FMS Bridge Visual. Some call it FMS Bridge visual, others call it RNAV bridge visual , some call it simply 28R visual in the ATC tape. Pretty loose given there is a Quiet Bridge Visual and Tipp Toe visual to 28R.
They would have to have DME/DME/IRU in lieu of GPS. They would have had to have it in the FMS to be approved to use it. Both the airline AND the crew have to be apprved. It is commonly used, so it is likely they were approved.
The 320 in question did not have GPS but is that really an excuse for a VFR approach at night under good visual conditions?
The response was to someone suggesting that Heads Up would be in order, hence my response that the ac does not appear to have GPS, so it is unlikely the airline would have the wherewithall to provide HU capabilites.