Sprinting can be an effective form of conditioing, but if the purpose is simply to develop strength/power for MMA then there are more effective and more specific alternatives for MMA training than sprinting. Try explosive bounds, stadium stair jumps, depth jumps, med ball drills, etc. If you are going to use sprints for power, then you should keep them to 5 seconds or so and do not go over the anaerobic threshold.
The method of using a maximal effort exercise and then a speed-strength exercise in series is known as the Stimulation Method and it's been around for a long time. I've seen it mentioned in Russian literature as far back as the early and mid 80s so it's definitely not something new.
The most effective and most intense form of this method uses a maximal effort exercise with a shock exercise in series. Keep in mind the stimulation method is extremely demanding on the CNS and is a very advanced method that should not be used except by experienced lifters. If you do use it, it should not be for more than 2-3 weeks at a time or you'll burn out your CNS quickly.
The way Dan John describes the method in the article is also not how they are performed by eastern european athletes. Instead, you perform 2-3 sets of a maximal effort exercise for 1-3 reps, then you perform 1-3 sets of the speed-strength exercise. This is considered 1 series and typically there are 2-4 total series done in a workout with 8-10 minutes rest between series. There is absolutely no reason to sprint or do the speed-strength exercise with no rest at all after each set of the max strength exercise as he suggests, in fact this would hinder explosive power development.
When done properly, you should see an acute drop in your strength and power during the concentrated loading phase followed by a strong rebound when you back off. There are probably not many people on this board who should be incorporating this method into their training but it is an extremely effective method when used properly.