The "MIDI Media Adaptation Layer for IEEE-1394" (aka 1394-MIDI or Firewire-MIDI) is part of the AM824 Protocol developed in conjunction with the 1394 Trade Association in 1999 (now known as IEC International Standard 61883, Part 6).The MMA Specification for MIDI over IEEE-1394 defines a standard way to place MIDI messages into an IEEE-1394 (aka FireWire) AM824 data packet so that products from various manufacturers can interoperate.
FireWire supports peer-to-peer connections (not requiring a computer) which are also common in MIDI systems, but is lacking a connection management standard, so most FireWire Audio/MIDI devices end up connected directly to computers instead.
While it could be more convenient for users if there was a "class compliant" FireWire-MIDI driver installed on every computer (one driver for all brands of devices) that is not necessary as long as device makers provide the necessary drivers for their own devices. Most FireWire audio and music device makers do provide their own drivers, and so might choose not to follow the MMA format for packetizing MIDI and audio over FireWire.
The IEEE-1394 AM824 Specification is also supported by IEEE-1722 (AVB Transport Protocol).