Good grief, people here make my head hurt. Let me get on my soap box and lecture a little history.
DirectX was developed in 1994! For games to run in their new Windows 95, that was coming out, you guess it, in the year 1995.
Games ran great in DOS, but they wanted programmers to develop them natively on Windows 95, so they made an API to replace DOS gaming. That API was called DirectX - maybe for Direct Access (Access sounds like it should have an X in it in English) or something - as it gave direct access to the graphics, mice, sound cards, etc and could replace DOS for gaming. Microsoft kept upgrading DirectX over the years – usually aligned with advancement in CPU and GPU technologies along with new versions of Windows. It was already DirectX 8 when the original Xbox came out. DirectX 9c for the Xbox 360, and DirectX 11.x, that will be upgraded later with year to DirectX 12 on the Xbox One.
And yes, the Xbox was named after DirectX, and as some said, originally called the DirectXBox. But they shorted it to Xbox. Just like a SteamBox is named after Steam.










