Drop into the hole to trigger an interactive cut scene ("Demon of the Past"). A monster like something out of Miyazaki grabs Kent and then comes after Lara.
NOTE: There's a stack of wooden crates in the next room. It's possible for Lara to get stuck between two of the crates, or even inside a crate, after this cut scene. If Lara gets stuck between crates, try pressing Interact to kick the crates aside. But if she's inside the crate, you may have to quit and reload a different save. To avoid this, do not try to jump and grab the rope during the chase scene. Just run forward off the edge and Lara will be safe. (Thanks to Stephanie, Gustavo and Joel for these tips.)