The idea that the Mayans are gone, both as a people and as a civilization, is based on a ridiculously reductive view of what the Mayans are - a storybook cliché rather than a living people. They've changed, certainly (but then, the French - or English, or Chinese, or Japanese, or... - of today bear little resemblance to the same civilization a thousand years ago!), but there is still a Mayan people with a distinct culture and a distinct identity. An independent polity is merely one possible way of expressing a civilization.
(Also, even if we were to say an independent polity is essential, "ancient" civilization is still a bit of a misnomer. We're not talking Rome and it's AD 470 or so fall here - we're talking a civilization that still existed as an independent nation 330 years ago (the last Mayan state, in the Peten basin of Guatemala, only fell in 1696). It would be very hard to justify calling a civilization that co-existed with Newton and Louis XIV "Ancient").
Now, Henri IS wrong, but the reason why he's wrong is simply that UU, UBs and the like should reflect the heydays of a civilization - which for the Mayans definitely is NOT anything in the 19th or 20th century. Mayans should absolutely have UUs and UBs that reflect the Classic and Post-Classic eras. But not because they somehow stopped existing after.