There's two things that increase stamina: cardio (fast, regular movement) and muscle endurance.
Pretty much any regular movement can do that - Shaolin training or anything else. You can do a few minutes every day up to the recommended at least 30 minutes of cardio that doctors recommend, and of course, more once you get the endurance going. Understand that of the kind of stuff you'll get, half will be movement based (punches, kicks, ec.) the other half will be stuff like stance work (Horse, cat, etc.) and that will improve the muscle endurance for your legs.
That short video you linked doesn't give me much to go on as to how well the guy teaches on the video, but there's a couple of things that are important for your training, even if you're just looking for endurance.
1) Correct stance - bad low stance work will do bad things to your knee cartilage over the long run.
2) Correct use of planting feet, especially with stomping or after a high kick. People can get nasty tendon issues from slamming their feet incorrectly or too much.
Both of these issues I've seen friends who have done Shaolin style training deal with, and it would be something to make sure you check in on.
If you are interested in things like correct form for form competition, or combative use of martial arts, you'll have a lot higher requirements to meet. At that point, I'd really recommend checking for an actual teacher, even if you only get a little bit of training with them so you have some kind of basis to use for any video or book references you take from there.
Understand that if you want more than cardio work, face to face instruction will take you far.