Voodoo 1 released 1996 with the Glide API in hardware.
Direct3D did not exist until DirectX 2. That release date was June 5, 1996.
There were other proprietary 3D chipset API's (S3's Virge was released several months before the Voodoo if I recall). Each 3d accelerator back then essentially had it's own API, and since most games were DOS based, you had a special executable for each one. Glide stood out because of ease of programming and the fact that the 3DFX boards were so much more powerful than the competition.
The nice thing about D3D back then is that it worked on pretty much every single 3D accelerator card. Yeah it was a sucky API. Glide was really fast but was 3DFX only and OpenGL didn't run on alot of cards back then.
Of course, that's not how it is now. That's the way MS works... create something that's compatible across the board, bundle it with the OS, force out the competition, then use it to dictate to the hardware manufacturers, and use it as a weapon against your own customers (you gotta buy Vista if you want D3D 10, but Vista will only run the older D3D in software emulation so all the game developers will drop it and try to force everyone to "upgrade").