It's conjecture either way. From everything I see, I think it's entirely possible that humanity could technically succeed like he says: conquer all known challenges on Earth, eliminate biological death even, and proceed to the stars.
However, it's also entirely possible we'll fail miserably and go extinct, not because any of these things are prevented by physics (they're not, except maybe exceeding lightspeed but you can always build a generation ship or use cryo-sleep etc. to work around that), but because our basic human nature prevents us: we'll fight with each other and annihilate ourselves, or we'll destroy our environment due to our recklessness and collective stupidity and shortsightedness, and that'll prevent us from making those achievements in time to survive.
Personally, I'd bet on the latter. I think it's highly likely we won't be around in 200 years, or if we are, we'll be back to the stone age and our population reduced to very small numbers. We're simply not showing that we have what it takes as a species to deal with global challenges successfully.