To retopo a mesh takes a lot of vertex pushing if you are doing it manually, you normally do it by hand. So you need to be pretty clued up with the product you are using. The demos make it look easy, but you are looking at the mouse of a modeling guru in those videos.
Mesh reduction or decimation, automatically strips away smaller polys, and keeps the general shape of the model. Unless you need to rig and animate the mesh. retopo-ing a mesh is a lot of unneeded work that can take several hours to do correctly. Whereas poly reduction can be done in a matter of minutes.
If you are part of a large team working on a serious project, re-topo is the way to go, since you get paid for your time. But for the "garage" game developer like myself, doing it quickly means I can spend less time on putting the resources together, and concentrate more on getting a working game out to market.
It's not a choice of methodology, it's a choice of practicality.
Edit: When I need to rig a mesh for animation, I simply slice the decimated mesh at prominent joints, such as the elbows and knees
Edit: There is also the other side of retopologing a mesh, when you need to merge two meshes together for something like a coin. But this is usually used for very high res displays, and seldom used in games. For example, in the image below, I used a r2d2 model from the warehouse, a VERY high poly "coin", and then used the Zbrush topology tool to make a commemorative coin to celebrate one of my sci-fi heroes.
