Yes, it's included in tix for all airlines. One possibility for explaining what happened to Mr. Vker comes to mind. The booths came down and taxes were supposed to start being included in tickets some time around last February, say Feb. 28th for sake of argument (I can't be bothered to find the exact date with a search because for present purposes it doesn't matter). The official policy was announced four to six months before the effective date. Once the announcement happened, as the airlines sold tickets, including FF tickets, the airlines should have collected the tax for departures from BKK after the effective date of the change, Feb. 28th. If the pax had purchased the ticket before the policy-announcement date, as might have happened with quite a number of FF award tix, the pax still had to pay the tax in cash upon departure; that was done by having check-in agents examine the tickets to see whether the tax had been paid and, if not, collect the tax (undoubtedly because the airline is liable to pay it to AoT regardless of whether the pax actually paid).

I'm no expert on reading the mumbo jumbo that appears on airline tickets. Old-fashioned paper tickets probably have a place where you can see the tax getting calculated and imposed. E-tickets may or may not. But it's worth a look. The 700 baht tax would be about $21.