It seems perfectly possible to design a program that could look up the cast of whatever show you're watching and display a list of actor's names and corresponding portraits/profile info from IMDB at the touch of a button.
The whole clicking on the actual actor onscreen thing seems possible also, but more complicated. The media would either have to be prepared so that the space each actor/relevant clickable object occupies onscreen for the entire movie or show is somehow cued to provide information, OR highly accurate and not very resource intensive (this seems unlikely) realtime facial/object recognition software would need to be employed. One sounds like too much extra work and the other sounds like it would need too much processing power.