I'm not sure the efficiency of the whole of humanity on earth and the efficiency of a comparably tiny colonial group is related in any way. There's a ton of momentum to overcome here on earth, and any change will need to occur across vast swaths of the population to be effective. That's an extremely tall order and it's extremely unlikely, as humans tend to ignore impending danger if there's no immediate consequence involved. Significant change will be seen at a generational pace at best.
Colonists, on the other hand, must be efficient if they wish to exist for longer than a few weeks, and they're a small and smart enough of a group that maintaining efficiency isn't an issue. Efficiency is a way of life for them. If anything, extremely low waste yet modern lifestyles will get their start in planetary colonies and make their way back to earth, not vice versa.
I think he means in the long run. His claim is that eventually you have a large group of average intelligence humans on our new planet and we decided to pursue colonization tech instead of sustainable energy and environment tech.
Of course, my bet is that we will reach the point where we can sustain a planet before we run out of planets (assuming we colonize a planet).
Well, if the Earth really gets that bad (e.g. the entire surface is all water, no land; or extremely destructive weather events; or too dark because sunlight can't reach our surface), it might actually be easier to set up self-contained (bubble) cities on another planet than on earth itself.
But if you're talking about terraforming, then if we could terraform another planet we could probably re-terraform earth itself.
We'd still have protection from cosmic radiation. Antarctica is far more livable than anywhere else off earth, but I don't see us living there in a self-sustained fashion.
Space exploration and colonisation is important, but it's not an answer for the Earth's problems. It may lead to new technologies that will help on earth though - not least the requirement for sustainability.
Even if all glaciers on Earth melted and went into the ocean, sea level would "only" grow by about 65 meters.
The issue with climate change is that higher temperature means more energy and thus more extreme climate. Plus there's desertification but that is, to some extent, a different issue.