He comes across as manic

A bit of context: that's not how he normally speaks.

There's another video (not publicly available, it's from a guest speech he did at one of Brendon Burchard's programs) where he gives the backstory on that talk. He was actually extremely nervous about giving that talk, for a couple different reasons. One, he felt it was a big honor and opportunity, two, he wanted to try to cram a lot of dense information into a twenty minute spot, and three, he got a bad introduction.

Specifically, he said the intro was something like, "Oh, and now here's Tony Robbins to motivate us", said in a sneering/dismissive tone... and he immediately felt some pressure to get the audience on his side -- a kind of pressure that he hasn't had to deal with in a public speaking engagement for quite some time. (Since normally he speaks to stadiums full of people who paid to come see him -- vs. an invited talk to a group where a lot of people -- perhaps most of the audience -- sees him as a shallow "motivator".)

IOW, the only drug you're seeing there is him feeling cornered and wanting to prove something --plus the time pressure of wanting to condense material he usually spends days on into twenty minutes. His normal way of speaking is a lot less fast paced, if still emotionally intense.

One of his time management programs that I bought over a decade ago had some interesting example schedules in it, that showed what he does to prepare for his time on stage (for programs where he's speaking all day) -- including nutrition, exercise, and renewal activities. It was impressive and well-thought out, but nothing that would require drugs.