[int_19h]

http://craig.theeislers.com/2006/02/20/directx-then-and-now-...

"Since multimedia on Windows had a bad reputation back then, we were adamant not to have our stuff associated with “multimedia” and so we called the first beta the “Game SDK”. We got the idea to name it DirectX because some reporter made of fun of how we had DirectDraw, DirectSound, and DirectPlay – Direct “X” they wrote. We took it and ran with it, and so every set of functionality became DirectSomethingOrOther (Direct3D, DirectInput, DirectSound3D all followed)."

And "direct", of course, was in a sense of direct access to the hardware (more direct than GDI, anyway).