String breakage is an age old problem that companies and guitar techs have made a lot of money on. Here is the honest truth. Strings break for three reasons:
1) A defective string (rare)
2) Flaws on the hardware (bridge, saddles, etc)
3) You are hitting the strings too hard!
We can usually rule out the first cause. This really is a rare occurrence. Unless you do what I do for a living, or are a touring musician who maintains their own gear, you probably won't have a defective string.
The holes in the bridge plate on a Fender Stratocaster type guitar, where the string comes through and onto the saddle is one possible culprit. Another is the saddle itself.
Gibson Tune-o-matic style bridges can often have similar issues with their saddles. They may not be notched correctly. Also, the break angle going from the bridge to the stop tail piece may be too aggressive.
If your guitar hasn't been setup professionally, the nut may also be at fault. Slots that are too narrow or cut at an aggressive angle will cause strings to break.
I should also mention the tuning machines. If they have sharp edges where the string goes through, it'll cut the string as you tune to pitch. However, this is also a rare occurrence.
Finally there is playing technique and pick choice. Something to consider, but shouldn't you be able to play how you want? I think so... and I'm here to help you do that. However, a string can only take so much force, even under ideal conditions. Changing to a thicker string or a thinner pick helps a great deal. Besides breaking less strings, your tone and playing technique may improve.
Now onto the video...