The conclusions/solutions drawn in the article seem to not match up with the data presented.
Anecdotally travel increasing with wealth is kind of obvious because it's a form of pent up demand. If I were able to, I'd visit fifty different countries every year.
In fact the thing that makes them different is precisely that difficulty.
But that doesn't imply that taxing luxury/first class travel would somehow fix that. I've literally never travelled in anything other than the worst possible class and yet my footprint is probably 10x most people I know.