At the time of the xbox 1, AMD had the Athlon K75 out, not very practical from a space standpoint, it also generated quite a lot of heat. MS really hesitated but in the end I think Intel offered such a cheap price for their P3/Cely that MS could'nt refuse.
The CPU in the XboX is really a mobile version of their P3/Cely CPUs, AMD never released a mobile version of their Athlon at that time.