"Everyone including myself (Ryan Hall) in the past taught this wrong."
Since my first days of BJJ and as an instructor today, I never learned or taught the triangle choke applying straight on. Sorry, just wanted to make that clear
Anyway, yes, it is a good idea to cut the angle and I do that as well as many of us here at Serra BJJ

However, that's not to say you can't finish it straight on. I think the reason your legs get tired is because you are relying on squeezing your legs and are probably very tense and in a rush to finish thus leading you to burn out very quickly. There are subtle details that make or break any technique. You can finish a triangle many different ways.
The video does show good technique and it is exactly the way I show it and was taught by Matt and Nick. BUT, there is more to it than just that.
I would love to explain in person because there is much more to it, and I will be here typing all day. So feel free to drop by Huntington and I'll show you or just ask my triangle master, Nick Serra!