The vine is a supernatural beingThe vine isn't just some crazy hyper-evolved plant, it's actually some kind of Eldritch Abomination. No mere plant could ever evolve the amazing abilities the vine displays, especially the understanding and use of languages it would only have heard spoken once or twice. Not to mention that most predators in nature are nowhere near as sadistic with their prey as the vine is with it's victims. It's clearly some kind of malevolent being.
The vine is an evolved carnivorous cannibalThe vine possibly fed off the remains and blood of the dead Mayan sacrifices of the pyramid and over time, it eventually absorbed all the nutrients and knowledge from the corpse which allowed itself to take over the pyramid. Over a period of a thousand years the combined knowledge of the dead and evolution made it a super efficent carnivore plant.
The vine's main food source would be (and likely still is) birdsIt likely evolved the ability to mimic bird calls, thus attracting them towards it. Of course, this makes the entire plot of the movie moot, but what else would the plant eat in the jungle besides tourists?
The Mayans have a symbiotic relationship with the vine creatureOne possibility is that the Mayans keep the vine creature in place in part by feeding it tourists. This doesn't seem too likely - the Mayans try to warn the party away from the overgrown temple before they touch the vines, and thus seal their fate. About the only real proof is that they don't Mercy Kill the entire party the moment they touch the vines; but if they did that, there wouldn't be much of a movie.