If you're evaluating linear slide options, REV Robotics has one which works with our extrusion building system you might want to look at:
http://www.revrobotics.com/15mm-linear-motion-kit/
We also have small pulley bearings for running the lift string:
http://www.revrobotics.com/rev-41-1368/
Our extrusion and linear slides are made specifically for FTC teams and are quite a bit cheaper than the 80/20 solution shown in your example video.
As Geetwo said, you need to run the numbers and see if your team can accept the amount of time it takes to lift with the correct gearing, but I think that using a
REV HD Hex Motor or
AndyMark NeveRest it would probably be fine.
We're also working on a linear slide building guide that will have more detailed examples and it should be available soon.
Please feel free to use the "Contact Us" option on the Rev Robotics website anytime; we're happy to provide technical support and guidance.