Would you do walking lunges for strength and power?

Regular lunges are probably better as far as increasing power and the transfer of the benefits to activities like running or power sports.

You could do plyometric lunges, which would increase your power development. In one such exercise, you start in the lunge position, jump as high as you can in the air and then switch legs so that you land with the other knee facing forward. Do at least 10 reps per leg but try to increase this by one rep every time you do it.

Power involves a strength and time component. Mark is right with the plyometric lunges; they incorporate a quick movement and a good amount of strength.

Walking lunges makes more sense for endurance training (many reps, longer exercise duration).

I have an issue with people doing walking lunges. I too have seen the video you are talking about, and you have to remember that Ronnie has the space outside to do the exercise. Not only is walking lunges not a required exercise, its not a good one to do in the gym environment with regards to space. Drop it buddy and do what Mark and Tim have said.