The use of the Cross Product in that example doesn't make much sense - in fact, I don't seem to be able to get that setup to work. The Value output of the Cross Product gives the average of the individual (X,Y,Z) elements of the vector. This could be argued to make sense if the X, Y, Z all have the same sign (ie, all positive or all negative) but as soon as you get a mix of different signs the result becomes effectively meaningless.
My own take on the 'Laser Line' issue would be to use a Point lamp with a small size (eg, 0.01) with the following nodes :
The 'Size' of the lamp will affect the width of the laser line, as will the value in the Less Than node.
Here a 'seed' vector is used to control the direction of the laser, adjustable via the Mapping node. This allows the vector to be easily rotated. The Dot Product compared the direction of the ray with the direction vector - if they are close enough (within the Less Than threshold) then the lamp emits light, otherwise it does not. The Ray Length is used to effectively tighten threshold the further the ray falls from the source - this ensures the ray doesn't 'spread' as it gets further from the source. Similarly, the Light Falloff node ensures the strength of the lamp remains constant regardless of distance.
This can produce the following result :