Been a while since I've done D3DX stuff, sorry. Let me see if I can explain it well enough so you can convert it:
emission.x would be the "X" value of the coordinate system around your emission point. It is a Vector3.
You scale, or set the length/magnitude, of the x vector to the random value between -1 and +1.
So, the result should be a vector3 again.
Do the same to the y coordinate axis and add that to the result of the x scaling.
You end up with a randomized vector3 in the x/y plane.
The final item is normalize the emission direction (+z) plus the offset vector which is scaled by the randomness value. Finally you scale the result by the desired velocity.
NOTE: Perhaps this will help, nothing other than scale, add or normalize are in use within this.