Unfortnately extrusions in maya are somewhat of a pain in the a$$ right now. Don't know why there have not been simpler tools to do this. Here is a thought on how to do this
1.) extrude a shape, in the extrusion options, select partial extrusion. Then you can use the min/max values of the subcurves to change the lenght of the extrude. I used this method for a growing beanstalk a month or two ago and it worked pretty good.
3.) if you need the extrusion to have some kind of "head" attached to it like you saw in the videos, that gets a lot trickier, espcially if the shape you want to grow is 3d like the beastalk i did or the shapes in the video. You might be able to attach a seperate head on a motion path and have it animate at the same rate as the body, then composite them back together? not a elegant solution , but possible (might even be able to render them both at the same time and skip the compositing stage) The trick would be blending the head object with the body.
kind of rambled there, but just wanted to throw out food for thought. I you only want to extrude a paper thin nurbs plane, then your in luck. Do my ribbon tutorial on the cow :)